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The 49-year-old took over as PSG boss in January – 14 months on from being sacked by Spurs – on a contract that has another year to run with the option of an extra 12 months.
He won the Trophee des Champion in just his third game in charge and followed that up with success in the Coupe de France with a 2-0 win over Monaco in the final this month.
However, last season's beaten finalist PSG exited the Champions League at the semi-final stage to Manchester City and finished second to shock title winners Lille in Ligue 1.
Widespread reports claimed Pochettino's relationship with sporting director Leonardo is already strained, and he is tempted to resign just four months into his reign.
That has prompted Spurs to make contact with the Argentinian, it is claimed, while Real Madrid – who confirmed Zinedine Zidane's exit on Thursday – have also been linked.
Tottenham are on the lookout for a new manager after parting company with Pochettino's successor, Jose Mourinho, last month.
But Pochettino, who spent five years at Tottenham before his departure in November 2019, appears to be planning for a long-term future at the Parc des Princes.
In an interview released on the French club's official website on Thursday, Pochettino said: "I'm happy with the way the players adapted to the changes.
"I think that with this way of working, and with the desire to be able to develop other kinds of ideas on the pitch, it will be possible to do great things in the future.
"I think that in football you are never satisfied. Because perfection doesn't exist. But we are always looking for that satisfaction that we can't find.
"I always believe that football challenges you every day and that from season to season you have to be better and better.
"But in a club like Paris Saint-Germain, you are forced to think that perfection or satisfaction can come and that winning is the only option.
"And for a club like ours, it's about winning, winning and winning. And then winning again. It's a feeling I always thought I'd like to have.
"It requires a amount of energy and always be sure that your priority is to be professional and that the difficulties and obstacles can always be overcome. I think that's the challenge, to impose that here."
PSG missed out on the Ligue 1 title for just the second time in nine seasons – the other instance being in 2016-17 when Monaco came out on top.
The Parisians finished the campaign with 82 points, which is their lowest tally over a complete season since 2011-12 when accumulating 79 points and finishing second.
It is just a second time a team has reached that total or better without being crowned champions after PSG themselves in 2016-17 (87 points).
And while PSG fell short of reaching a second successive Champions League final, they did knock out holders Bayern Munich and Barcelona en route to the semi-finals.
Pochettino, who succeeded Thomas Tuchel in the French capital, said: "Of course I'm proud of the team's effort, because only we know what state the team was in and what we were capable of.
"I'm proud of all the people involved, not just the players, but all the staff at the club, everybody, because I think the effort was incredible.
"Winning the Trophee des Champions, winning the Coupe de France, reaching the semi-final of the Champions League, without being in your best form.
"We also fought until the last game with the possibility of winning the championship, and given the conditions in which we arrived in January, we should be proud of everything."