Paris Mayor Anne Hidalgo criticised Paris Saint-Germain's approach to the row over Kylian Mbappé's future, with the star forward training with the reserves after he refused to extend his contract at the club.

Mbappé was left out of PSG's preseason tour of Japan, with club president Nasser Al-Khelaifi demanding he either agree to a new deal beyond June 2024 or accept a departure this summer.

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PSG have received a world-record €300 million ($332m) bid for Mbappé from Al Hilal, but sources have told ESPN the France international has not held talks over a move with the Saudi Pro League side.

Hidalgo entered the debate over Mbappé's future on Tuesday in an interview with French radio station RMC and questioned PSG's hardline stance with the player.

"I don't understand what PSG are playing at," Hidalgo said. "Kylian Mbappé is the best player in the world. I'll admit that I don't understand it at all."

"Kylian is an extraordinary player and we have to keep him in Paris," she added. "I think it's also his wish to remain here as long as possible. The question is: what are PSG doing?"

Sources have told ESPN that despite being frozen out of the first team, Mbappé has appeared happy and unconcerned in training this week.

The player has publicly said that his preference is to remain in Paris for one more season until his contract expires, but PSG are unwilling to entertain him leaving on a free transfer.

Sources told ESPN that Al Hilal are the only club to have made a formal bid for Mbappé, but in the event of a move, he is only interested in joining Real Madrid.

Madrid have been tracking Mbappé for over a decade and tried to sign him in each of the last two summer transfer windows.

The LaLiga club's No. 9 shirt is now vacant after Karim Benzema left for Saudi Arabia at the end of last season.

However Madrid are waiting for Mbappé or PSG to make the first move, sources have told ESPN.

They are aware that Mbappé favours a move to the Spanish capital -- and have been in regular contact in recent months -- but are acting cautiously after the player's last-minute decision to stay at PSG last summer.