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The German coach was dismissed by the Blues earlier this month after a poor start to the season, with the 1-0 defeat to Dinamo Zagreb on 6 September proving to be his final game in charge.
Graham Potter was then appointed as his successor, with Chelsea paying a record £21 million compensation fee to Brighton for the coach and his staff.
Tuchel is still living near Chelsea's Cobham training ground and his daughters go to school in Surrey.
However, according to The Telegraph, the former Mainz manager is unsure when he must leave the United Kingdom because of Brexit rules.
Tuchel took the reins at Chelsea in January 2021 and he arrived on a post-Brexit Governing Body Endorsement visa.
Chelsea had to file a special application in order for Tuchel and his staff to be allowed access into the country after a rule change.
It's said that he would be able to stay on these shores for 90 days but there has been no official confirmation from the relevant parties like the FA or Home Office.
Talks are ongoing and Tuchel, who is "happy and comfortable" in the UK, is still weighing up his options going forward given the uncertain predicament.
A representative for Tuchel told the Telegraph: "We will act in accordance with UK rules and adapt all future plans. Final decisions are not made yet.”
He has been linked with a quick return to management, with both Bayern Munich and Juventus said to be keeping tabs.
When he was relieved of his duties at Paris Saint-Germain, Tuchel was back in the management game in just over a month.
Yet he has taken sabbaticals on two separate occasions after leaving Borussia Dortmund and Mainz respectively.
The 49-year-old guided Chelsea to second Champions League triumph when they beat Manchester City in Porto for months into his tenure and followed it up with Super Cup and Club World Cup successes.
He also reached the FA Cup and Carabao Cup finals and finished with a 60 per cent win ratio.