Pochettino has been out of work since being sacked by Spurs last November after five years in charge of the club in north London.
The Argentine boss spent two years of his playing career at PSG, winning the 2001 UEFA Intertoto Cup.
Sources have told ESPN that a number of players expected Tuchel to get the sack, but he liked it in the locker room.
Sources also said Tuchel held meetings with club president Nasser Al-Khelaifi and sporting director Leonardo and it was decided to replace him last week due to his tension with Leonardo and lack of playing style.
The French champions suffered a 1-0 home defeat at the hands of the Lyon table on December 13 before a goalless draw at Lille on Sunday.
The departure comes four months after Tuchel led the club to their first Champions League final, where they lost to Bayern Munich in Lisbon.
Tuchel was appointed on a two-year contract in 2018, replacing Unai Emery, and won the Ligue 1 title in his first campaign before claiming a domestic treble in his second as well as reaching the Champions League final.
But his third season in Paris was overshadowed by a disagreement with Leonardo over player recruitment.
In October, Tuchel publicly criticized Leonardo, saying: “We are losing too many players on free transfers. It is too much. We can not ask this team for the same as we did last season.”
Leonardo reacted the following day after PSG’s 6-1 win against Anger in Ligue 1: “I did not like his comments. The club did not like them either.
“We have to understand the moment we go through. If someone is not happy, it’s easy – we can talk. But if you decide to stay, you have to respect the people above you.”
Thiago Silva, Eric Maxim Choupo-Moting, Thomas Meunier, Edinson Cavani, Tanguy Kouassi and Adil Aouchiche all left PSG over the summer, even though they signed Alessandro Florenzi, Moise Cain and Danilo Pereira lent and Rafinha on a free transfer.
Tuchel parted Borussia Dortmund in May 2017 amid reported disagreements with the club hierarchy, despite leading the club to the DFB Cup title three days earlier.
PSG return to action when faced with another turn Saint-Etienne on January 6th.