Chelsea sacked Tuchel on September 7 after a 1-0 defeat to Dinamo Zagreb in the UEFA Champions League.
He led the Blues to Champions League glory in 2021 before winning the FIFA Club World Cup and UEFA Super Cup in 2022.
However, Chelsea made a poor start to the current season under the German, which saw them win three and lose as many after seven matches.
There has been speculation over where Tuchel may head next, and the England job has been touted as a possibility.
The Three Lions are currently managed by Gareth Southgate and travel to Qatar for the 2022 FIFA World Cup in late November.
Southgate is under pressure following a woeful UEFA Nations League campaign which saw his side draw three and lose as many. They scored just two goals from open play in the tournament, leading many to question Southgate's tactics.
The England manager even admitted that his position was not safe despite having signed a new three-year deal just last year, he said:
"I am not foolish. I know ultimately I will be judged on what happens at that World Cup."
"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."
Southgate's current contract runs until 2024 but his comments hint that should England fail to deliver at the World Cup, he may be heading towards the exit door.
Former Chelsea boss Tuchel would be a brilliant appointment for England
Tuchel is a manager with vast experience having coached in the Premier League, Ligue 1 and the Bundesliga.
He was acclaimed for his quick turnaround at Chelsea which saw him win the Champions League just four months into his tenure.
The German won two Ligue 1 titles and a Coupe de France with PSG. He also led the Parisians to the final of the Champions League in 2020.
Tuchel also lifted the DFB-Pokal with Borussia Dortmund in 2017 so evidently his resume speaks for itself. The former PSG manager could be monitoring England's progress at the World Cup closely.