The Brazilian also denied reports that PSG had approached former Real Madrid boss Zinedine Zidane, saying he has had "no contact" with the Frenchman.
British media reports earlier this week suggested that former Tottenham boss Pochettino could be persuaded to leave Paris and join Man United mid-season.
But it has since emerged that German Ralf Rangnick is set to take over at Old Trafford until the end of the season, with his lawyer telling AFP subsidiary SID on Friday that the final points of a deal are being ironed out.
That would leave Pochettino at the Parc des Princes at least until June when it is reported Rangnick would take a consultant's role at United.
"I think it's important to clarify the situation given the amount of false information circulating. Mauricio Pochettino is under contract with the club until 2023," Leonardo told AFP.
"We don't want Pochettino to leave. He's never asked to leave and no club has contacted us in relation to him."
There have been consistent rumours that Pochettino is unhappy in the French capital and he was also briefly linked with a shock return to Spurs earlier this year.
But the Argentinian said earlier this week that he is "so happy in PSG" and he is not planning to quit before the end of his contract.
Reports have said PSG could move for Zidane, whenever Pochettino leaves.
One French media report even claimed that PSG, including Leonardo, held a secret meeting with Zidane at a hotel in Paris and that negotiations have been ongoing for several weeks.
"It's ridiculous to imagine that a meeting with Zinedine Zidane could have taken place in a big hotel in Paris in front of the eyes of everyone," Leonardo said.
"We have a lot of respect for Zinedine Zidane, what he did as a player and coach, but I can tell you very clearly that there is no contact and that no meeting with him took place."
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