However, with Messi having made clear that his future at Barcelona is very much up in the air, many feel that Manchester City and PSG are the only two clubs with the financial power to cover the six-time Ballon d'Or winner's wages.
Pochettino, who has been out of work since being sacked by Tottenham in November 2019, has signed a deal until June 30 2022, with the option of an extra year.
Pochettino's first match in the PSG dugout will be Wednesday's Ligue 1 trip to Saint-Etienne.
The Englishman has been close to PSG for nearly a month, which is trying to get a loan, and the Frenchman entered this last week but, according to the Daily Mail, the English club has closed the exit door to both players.
Inter Milan playmaker Christian Eriksen, again well down the pecking order at his current club, has also been linked with a reunion with Pochettino at the Ligue 1 giants.
Sacked with six months left on his contract, Tuchel is unlikely to be missed by supporters of the Parisian club despite leading them to the Champions League final for the first time in their history.
PSG chairman and chief executive Nasser Al-Khelaifi said Pochettino's return "fits perfectly with our ambitions", adding: "It will be another exciting chapter for the club and one I am positive the fans will enjoy". "PSG is a team I always wanted to coach, it was one of my targets".
"Of course Tottenham, today, is too". It [Spurs] is an awesome club and we have unbelievable memories from there.
Pochettino moved to Tottenham in 2014, after the club had finished sixth in the Premier League in an erratic campaign that saw them replace Andre Villas-Boas with Tim Sherwood.
"It is hard to be objective with Tottenham". Spurs is still in our hearts and we love Tottenham. It is a relationship that is never going to stop.
Could Alli join Poch at PSG?
Tottenham are adamant that Dele Alli and Hugo Lloris will not be allowed to leave in January.
According to the same story, PSG are prepared to back Pochettino in the January market after the Argentinian took over the reins from Thomas Tuchel this month.
Dele Alli and Mauricio Pochettino.
Pochettino's success in north London was the key factor behind PSG's decision to appoint him. At Espanyol, Southampton and Spurs, he was tasked to build from the ground up with emphasis on bringing young players through. "I am not so sure".
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