The 47-year-old was fired by PSG last week, just four months after leading them to the final of the Champions League.
Former Tottenham manager, Mauricio Pochettino, will now replace him at the Parc des Princes.
Tuchel has received a pay-off of £5.4million and would be free to take over at another club right away.
It is understood Chelsea could be that club if Frank Lampard cannot arrest their downturn in form, that has seen three defeats in four Premier League matches ahead of Tuesday’s home fixture against Aston Villa.
Tuchel would be interested in the job if the opportunity arose and would relish the opportunity to work with Germany internationals Timo Werner, Kai Havertz and Antonio Rudiger.
There was contact between Chelsea and Tuchel when he left Borussia Dortmund back in 2017.
