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The reports said that PSG bosses told Tuchel after Wednesday's 4-0 league win against Strasbourg that he has to go, six months before the expiration of his three-year contract at the French champions.
Argentine Pochettino of Argentina is to take over at the club he played for 2001-2003, with French sports paper
l'Equipe saying the 48-year-old has agreed to a contract until 2023.
Pochettino has been out of coaching since he had to go at Spurs in November 2019.
PSG were yet to make an official announcement.
The German Tuchel, 47, came to PSG in 2018 and won back-to-back league titles with them, plus the French Cup and League Cup last season. He led them into the Champions League final for the first time in summer, losing 1-0 to Bayern Munich.