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It has been claimed Pochettino, who only took over from Thomas Tuchel at Parc des Princes in January, has told the Ligue 1 giants that he wishes to terminate his contract.
The Argentine, whose contract runs until next year with the option of a further 12 months, has been linked with a return to Tottenham or a move to Real Madrid to succeed Zinedine Zidane.
However, it has also been reported that Pochettino would be prepared to stay at PSG for another season if required as he does not wish to sour his relationship with a club where he spent two and a half years as a player.
Leonardo said: "Mauricio Pochettino has two years on his contract with PSG and we're very happy with him."
Speculation around Pochettino emerged after he was unable to guide PSG to the Ligue 1 title, with Lille finishing one point above them to be crowned champions for the first time in 10 years.
It was also beaten by Manchester City in the Champions League semi-finals, having lost to Bayern Munich in the final last season.
Pochettino left Spurs in November 2019 despite leading them to the Champions League final that year as poor domestic results left his position untenable.
However, Spurs are said to be interested in bringing him back to north London, where he achieved four top-four finishes in five seasons, twice as many as the club managed in their previous 22 Premier League campaigns.
Pochettino was previously linked with Madrid and Los Blancos are again looking for a new coach after Zidane stepped down at the end of a trophyless season.
Former Inter boss Antonio Conte and academy coach Raul have also been tipped for the job at the Santiago Bernabeu.