The 48-year-old – who was Paris Saint-Germain’s skipper during his spell at the Ligue 1 side – has been out of a job since being sacked by Spurs last November.
And it has been claimed that he would welcome a move back to France to take charge of Les Parisiens.
According to talkSPORT, German gaffer Tuchel is under pressure at PSG.
That is despite the club sitting top of the French table and almost sealing a place in the Champions League knockout stages with last night’s win over Manchester United.
His contract expires at the end of the season, and it has been claimed that club chiefs are already looking to replace the ex-Borussia Dortmund boss.
One of those who could succeed Tuchel is Pochettino, who has been heavily linked with replacing Zinedine Zidane at Real Madrid.
It has been stated that Zizou has just four games to save his job at the Bernabeu with Los Blancos in danger of failing to qualify for the Champions League Round of 16.
But Pochettino could be tempted back to PSG, as French football expert Julien Laurens said: “The pressure on Thomas Tuchel is big.
“He’s out of contract in June and he knows that he’s not going to get an extension, or that it’s very, very unlikely now.”
Before adding: “Pochettino has been very clever in the way that he’s waiting. He could have gone back to management very early on but he waited.
“He really wanted to get the right project and the right club.
“Real Madrid would be interesting for him, we know how close he is to Florentino Perez.
“But he has really good ties with PSG, he was their player, their captain, and he loves Paris as a city and a football club.
“That could be very interesting , I think it’s a very attractive club for any manager.
“I think Manchester United is still in the back of his mind, because maybe Ole Gunnar Solksajer has lasted longer than all of us expected, but certainly he [Pochettino] would be high on their list.”
Pochettino has been heavily linked with a move to Old Trafford, but that now seems unlikely after Solskjaer received a vote of confidence from Ed Woodward.