Manchester United are interested in signing Italy international right-back Matteo Darmian, sources in Italy told ESPN FC.
Torino say they have received three offers for the 25-year-old and that the defender's future must be decided by Sunday.
United have turned their attention to Darmian after ruling out a move for Nathaniel Clyne, who had been a target but subsequently left Southampton for Liverpool, and after Dani Alves signed a new contract at Barcelona .
Everton's Seamus Coleman is also on United's radar as manager Louis van Gaal continues his search for a right-back, but Darmian has now emerged as the favourite to join United.
The former Milan and Palermo player has spent four years at Torino and has become Italy's first-choice right-back, having been voted the Azzurri's best player of 2014 by the fans.
Darmian has also been linked with Bayern Munich and Napoli, and Torino president Urban Cairo told La Stampa: "Everyone who comes to the preseason training camp will remain with us for the rest of the season.
"Sunday will be the deadline. Three offers have arrived for Darmian, but out of respect for the clubs who have made them, I won't reveal who they are. Darmian is an extraordinary player who will want to try and win the Champions League one day."
Cairo added: "I told him last year after the World Cup: 'Matteo, even if bids come in for you, we cannot sell you this year.' We already had [Ciro] Immobile and [Alessio] Cerci leaving so I couldn't allow us to lose another excellent player, but I said: 'Next year, we can talk about it again.'"
The Torino president had said in April that Darmian would only leave if the club received a "crazy" offer. Italy's Mediaset television has said the club are seeking €18 million for the full-back.
United have made it a priority to recruit a specialist right-back, with winger Antonio Valencia having spent much of last season operating as a makeshift defender.
Rafael da Silva, who fell out of favour under Van Gaal and did not start a Premier League game since October, is expected to leave Old Trafford this summer, with Galatasaray, Fiorentina and Napoli reportedly interested in the Brazilian.
ESPN FC's Italy correspondent, Ben Gladwell, contributed to this report