Tuchel has been out of management after being sacked by Chelsea on September 7, and speculation has grown about where he will end up next.
The German remains open to continuing his managerial career in England but appears to have rejected the advances of two unnamed Premier League clubs.
Wolverhampton Wanderers and Bournemouth are the only clubs currently without a permanent manager in the league.
Wolves sacked Bruno Lage on October 2, with the side 17th in the league.
Meanwhile, Bournemouth parted ways with Scott Parker in September after a 9-0 humbling against Liverpool.
Tuchel became a huge hit at Stamford Bridge during his tenure in charge of the Blues, winning the UEFA Champions League in 2021.
He also won the FIFA Club World Cup and the UEFA Super Cup during his time in west London.
However, Chelsea made a disappointing start to the season under his tutelage, losing two league games and sitting sixth in the table.
They were defeated 1-0 by Dinamo Zagreb in the Champions League on October 6 which turned out to be Tuchel's last game in charge.
The former Paris Saint-Germain boss has remained quiet following his departure, although he admitted the devastation of losing his job.
He wrote on his Twitter account:
"I am devastated that my time at Chelsea has come to an end. This is a club where I felt at home, both professionally and personally. Thank you so much to all the staff, the players and the supporters for making me feel very welcome from the start."
Ex-Chelsea boss Tuchel in England frame
Gareth Southgate will lead the Three Lions into Qatar for the 2022 FIFA World Cup at the end of November but speculation is growing over his future.
England were woeful in their UEFA Nations League campaign, losing three and drawing as many of their six fixtures.
Tuchel has been touted as a potential successor should England fail to deliver in Qatar and the German is reportedly open to coaching the Three Lions.
Southgate's coaching has drawn criticism and he has admitted that his job is not wholly safe despite being contracted until 2024, saying:
"Contracts are irrelevant in football because managers can have three, four, five year contracts and you accept that, if results are not good enough it is time to go your separate ways. Why would I be any different? I am not arrogant enough to think that my contract is going to protect me in any way."