The 51-year-old has been out of management since leaving his post at the Allianz Arena at the end of last season, having only been able to muster a third-placed finish with the previously perennial Bundesliga champions.
Tuchel was never expected to be short of offers to make an immediate return to management, but the 2020-21 Champions League winner has been biding his time and is yet to commit to a new job.
A stint at Man United has been strongly mooted for Tuchel, though, as the Red Devils are being tipped to part ways with the under-fire Erik ten Hag after a disastrous start to the campaign.
No decision on Ten Hag's future is thought to have been made at a summit of Man United chiefs earlier this week, but Tuchel is already said to have chosen his first signing if he was to take the job.
Tuchel 'negotiating' to become England manager
However, Bild journalist Christian Falk now reports that the German is locked in negotiations with the FA to become the next head coach of the England national team instead.
The governing body are on the lookout for a permanent successor to Gareth Southgate, who stepped down from his position after leading his nation to back-to-back European Championship finals, albeit while losing both of them.
While Tuchel was available immediately, England appointed Under-21s head coach Lee Carsley on a temporary basis in order to give them a few months to scope out candidates and come to an informed decision.
Carsley made a positive start to his reign with 2-0 wins over Finland and the Republic of Ireland, but the 50-year-old then oversaw a surprise 2-1 defeat to Greece in Thursday's UEFA Nations League battle.
Carsley suggested afterwards that he did not want to be given the job on a permanent basis, although he will be in the hotseat until at least the end of the year as the FA continue their search.
Ten Hag stance 'revealed' amid exit talk
With Ten Hag having not received any firm communication from the powers-that-be that his job is under any immediate threat, the Manchester Evening News reports that he is still expecting to take charge of next weekend's clash with Brentford.
However, one member of the Man United hierarchy is alleged to have pushed for his sacking during their meeting this week, and he remains a man under severe pressure at this moment in time.
Meanwhile, the FA are still said to view Carsley as a candidate for the head coach position, according to the Daily Mail, even if the loss to Greece will go down as a mark against him.
Eddie Howe and Graham Potter are also believed to be high on England's shortlist of possible head coaches, as is Pep Guardiola, who will be free to leave Manchester City in 2025 as things stand.