FOXBOROUGH, Mass. -- Quick-hit thoughts and notes around the New England Patriots and NFL:

1. D-Hop dynamics: The Patriots are scheduled to host free agent wide receiver DeAndre Hopkins on a visit this week, giving coach Bill Belichick a chance to connect with a player he’s long admired. It should serve as a fact-finding mission for both, with Hopkins arriving after a visit with the Titans and Belichick having had a full spring to assess his team’s skill-position personnel.

Will it be a fit?

Here is one view of the key dynamics in play:

Patriots culture: Belichick annually places a heavy emphasis on culture. This was one of the lesser-highlighted aspects of the team’s free agent approach this offseason, as there was a feeling in some team circles that the culture needed a boost after a challenging 2022 season. One example: Veteran offensive tackle Riley Reiff (1 year, $9 million) has quickly emerged as a favorite with his steady everyday presence.

As for Hopkins, who would make any team better on the field, how he would fit into the team culture will be one of Belichick’s most important calculations.

When the Patriots make a significant investment in a player, they are essentially telling everyone in the locker room what they value most. Belichick believes heavily in practice. He annually says that the best way for players to improve is practice.

But word out of Arizona is that the 31-year-old Hopkins, who was due to make $19 million in 2023 before his release, did not like to practice. And it’s perhaps telling that as the Cardinals are attempting to establish a new culture under first-year coach Jonathan Gannon and general manager Monti Ossenfort, they voluntarily subtracted Hopkins from the mix.

D-Hop’s priorities: Hopkins should have a good feel for what life would be like in New England under offensive coordinator Bill O’Brien, having played for him in Houston from 2014 to 2019 when O’Brien was head coach. Hopkins was named first-team All-Pro three times while playing in O’Brien’s offense, totaling more than 1,000 receiving yards in five seasons before he was traded to Arizona.

Time away can sometimes spark greater appreciation from a player, and Hopkins’ willingness to visit the Patriots -- in addition to hopes of generating a market for himself -- might reflect that. He said on the “I Am Athlete” podcast that some of the things he’s seeking in his new team are “stable management, a QB who loves the game and brings everybody on board with him, and a great defense.”

A case can be made the Patriots check those boxes.

Left unsaid, however, is how Hopkins views his potential contract relative to those desires.

Financial market: Odell Beckham Jr.’s one-year, $15 million deal with the Ravens that could be worth up to $18 million would be a coup for Hopkins. Beckham seemed to benefit from a competitive bidding situation, and perhaps the Ravens’ needed to placate quarterback Lamar Jackson as they navigated his contract stalemate at the time.

What are the chances that type of perfect storm unfolds for Hopkins? It seems like a longer shot, especially in New England.

A one-year, $10 million contract that would be worth up to $12 million to $13 million might be a more reasonable target for Hopkins (and a team like the Patriots). But if joining a contender is of greater importance to him than the contract, a la Randy Moss in 2007, that would change the dynamic and give top-tier teams with less financial flexibility a chance to get in the mix (e.g., the Bills).

When the Patriots landed Moss, he was so motivated for the fresh start (and playing with Tom Brady) that financial terms weren’t a top priority for him.

Hopkins' approach will be telling in this regard -- how does he balance pursuit of a first-ever Super Bowl ring with the most lucrative contract?

2. Receivers on the mend: If the Patriots sign Hopkins, one line of thinking is that it could mean another receiver on the team could be let go, with Kendrick Bourne an oft-mentioned possibility. But considering the team has been cautious with offseason addition JuJu Smith-Schuster (a knee injury knocked him out of the AFC Championship Game) this spring by keeping him off the field, and a source said Tyquan Thornton is managing a soft-tissue-related injury after he was active early in OTAs, a case could be made that voluntarily thinning the receiver ranks would be a risk not worth taking.

3. Eyes on Trent: After showing up for an early voluntary organized team activity, starting left tackle Trent Brown hasn’t been around the team of late. So it’s been five-year veteran Calvin Anderson at left tackle, Reiff at right tackle, with Conor McDermott the next tackle in the mix. Second-year man Andrew Stueber (2022 seventh round, Michigan) and rookie Sidy Sow (fourth round, Eastern Michigan) add depth. Thus, where Brown slots into the mix at this week’s mandatory minicamp -- which is essentially an extension of organized team activities -- bears watching.

4. Revamped offense: The communication, synergy and rhythm of OC O’Brien’s attack has been notable to reporters watching practice, and more importantly, to the players in the huddle.

“It feels good, it feels fast,” wide receiver Bourne said. “Everybody is on the same page and you can see the growth already. That’s the exciting part. I feel like we’re going to know exactly what we’re doing, and who we are, quickly.”

5. Mac report: On one play in Friday’s practice as the offense generated momentum moving the ball down the field, quarterback Mac Jones hurried everyone to the line of scrimmage and then drew defensive tackle Daniel Ekuale offsides with a hard count. Jones thrust his right arm forward and pointed his right index finger to signal a 5-yard penalty and first down.

The play reflected, in part, Jones’ comfort and command this spring over eight practices, three of which were lower tempo. Teammates have taken note.

“Mac's awesome. That’s my guy,” said tight end Mike Gesicki. “He’s been incredible as a leader and been great out there physically throwing the ball, and timing, and throwing a very catchable ball. And he likes to have fun. It’s been a cool offseason for us trying to jell and get on the same page.”

6. Mapu’s role: Third-round pick Marte Mapu of Sacramento State has been intriguing to watch this spring, playing linebacker (where his 6-foot-3, 218-pound build is undersized) and safety (where he intercepted Bailey Zappe on Friday and got his hands on two other passes).

“I think it kind of goes to the evolution of the game -- having guys being able to play multiple positions and growing up playing multiple positions in high school and college,” veteran safety Adrian Phillips said. “Seeing him out on the field, it all looks comfortable to him. It looks like stuff he’s seen before.”

“Depending on what package we’re in, what personnel is on the field, they’re interchangeable. So learning both is essential,” safety Kyle Dugger added.

7. AFC East: Last week, Patriots owner Robert Kraft referred to the AFC East as the most difficult division in the NFL, from top to bottom, and it’s hard to argue his point. The AFC North and NFC East warrant consideration, but it’s been a long time since the AFC East has been this stacked. In a reflection of that, the Patriots have just an 8% chance to win the division based on ESPN’s Football Power Index, despite being the 16th-best team in the league in the model’s view.

8. They said it: “Just a bad year. I felt like I didn’t get better. I don’t really go off stats; I just go off how I feel, how I looked, and I just wasn’t in a good place. I just want to avoid that. It’s always good to learn from hard times.” -- Bourne on his 2022 season (41.9% playing time, 35 receptions for 434 yards, 1 TD)

9. Squib kicks: In light of the NFL’s new kickoff rule that allows fair catches to be spotted at the 25-yard line, it was more than a passing note that veteran Nick Folk and rookie Chad Ryland spent time after Friday’s practice working on squib kicks. Special teams coaches across the NFL figure to experiment with different possibilities on kickoffs this offseason, and Joe Judge has emerged as a leading presence in that area in New England this spring.

10. Did you know? Since sacks became an official statistic in 1982, former Patriots outside linebacker Willie McGinest remains the NFL’s all-time leader in postseason sacks with 16. Frank Clark, who signed with the Broncos last week, is the closest active player with 13.5.