Kylian Mbappé trained with other out-of-favour Paris Saint-Germain players on Tuesday and remains unconcerned about his ongoing standoff with the club over his future, sources told ESPN.
The rest of PSG's first-team squad are currently on a preseason tour of Japan, where they drew 0-0 with Cristiano Ronaldo's Al Nassr in Osaka on Tuesday.
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PSG have received a world-record €300 million ($332m) transfer bid for Mbappé from Al Hilal, after the superstar forward said that he would not be extending his deal in Paris beyond next summer.
However if the clubs were to reach an agreement, Mbappé, 24, would still have to accept the move himself, and agree terms with the Saudi Pro League club.
Sources told ESPN that Al Hilal have not contacted the France international directly and he would not be open to the switch, in any case.
Al Hilal are the only team to submit a formal offer for Mbappé, sources said, but the player is only interested in joining Real Madrid.
Mbappé was left out of PSG's touring party for Japan as a consequence of his refusal to sign a new contract.
Club president Nasser Al Khelaifi has said that PSG will not accept Mbappé leaving on a free transfer in 2024, and his options are either renewing or accepting a move this summer.
Mbappé trained on Tuesday with other players who are not in new PSG coach Luis Enrique's plans, such as midfielders Leandro Paredes and Georginio Wijnaldum.
He appeared happy and unconcerned about the situation, sources said.
A report from the French newspaper L'Equipe on Monday claimed that Barcelona were set to join the race to sign Mbappé.
The LaLiga club's tight finances make such a deal unaffordable at present, sources told ESPN, suggesting that the report was an attempt to put pressure on Real Madrid.
Mbappé has been Madrid's long-term top target -- they failed in efforts to sign him in 2022 and 2021 -- and the club have a vacancy in attack after the departure of Karim Benzema.
However, the club want the player or PSG to make the first move, sources told ESPN, before negotiations can begin.
Madrid are keen to avoid a repeat of what happened last summer, when a surprise, last-minute change of heart saw Mbappé snub them to sign a new PSG contract.
They are aware that they are Mbappé's priority for his next club, sources told ESPN, and have remained in constant contact with the player, especially over the last two months.