The 51-year-old has been out of management since leaving his post at Bayern Munich at the end of last season, following a disappointing trophyless campaign which culminated with a third-placed finish in the Bundesliga.
Tuchel, who has also managed Chelsea, Paris Saint-Germain and Borussia Dortmund, has since been linked with several high-profile jobs, including Manchester United amidst uncertainty over the future of Erik ten Hag.
However, as things stand, Red Devils chief Sir Jim Ratcliffe would allegedly prefer to appoint Zinedine Zidane as the club's new manager should they decide to part ways with Ten Hag in the near future.
The prospect of taking an international job has also been mooted for Tuchel, with reports from Germany claiming that he has been 'locked in negotiations' with the FA to become the next England head coach.
Tuchel a 'primary choice' for FA despite Guardiola links
It was initially reported by Sky Sports News that there had been no formal approach from the FA to any of the proposed leading candidates about the vacant managerial position.
However, they now claim that the FA have accelerated their search for a successor to Gareth Southgate in recent days and are in talks with Tuchel's representatives.
Manchester City manager Pep Guardiola is also understood to have been sounded out, and while he is said to be 'hugely admired' by the FA, the Catalan coach is not thought to be an active candidate and is leaning towards extending his contract at the Etihad Stadium.
Now, Tuchel is believed to be the FA's primary choice to become the permanent England manager, although details about his contract are yet to be agreed.
FA technical director John McDermott is keen to appoint a coach with a proven track record of winning trophies, and Tuchel fits that desired profile having won a total of 11 pieces of silverware in charge of four different clubs.
Carsley confusion forcing FA to step up Tuchel pursuit?
After winning the DFB-Pokal with Dortmund, Tuchel celebrated top-flight glory with both PSG and Bayern among other domestic honours, while he also lifted the Champions League, UEFA Super Cup and FIFA Club World Cup in charge of Chelsea.
The FA's decision to step up their pursuit of a new first-team boss is said to have been made following England's shock 2-1 defeat at home to Greece in the UEFA Nations League last week.
Lee Carsley was placed in interim charge in August and has taken charge of four senior matches in the Nations League, but the 50-year-old has been reluctant to confirm or deny whether he would be interested in taking the role on a full-time basis.
After leaving Bayern, Tuchel was placed on gardening leave by the Bundesliga giants, buy Sky Sports News claims that the FA would not be required to pay any compensation should they decide to appoint the German.
Tuchel could become just the third non-English manager to take charge of the senior men's England team after Sven-Goran Eriksson and Fabio Capello.