Sources have told ESPN that Potter heads a shortlist for the job which also includes Mauricio Pochettino and Zinedine Zidane.
According to sources, former Tottenham Hotspur boss Pochettino is interested in the job but believes Potter is the frontrunner.
The exact figure is as yet unclear but sources suggest Chelsea would need to pay at least £10 million to release Potter from his deal at Brighton, where is under contract until 2025.
Chelsea are keen to move quickly to appoint Tuchel's successor with their next game at Fulham on Saturday lunchtime.
Brighton finished in ninth place with 51 points last season -- their highest tally in the Premier League.
Potter, 47, has won plaudits for Brighton's attacking style of play, and their progress has continued unabated this season despite losing midfielder Yves Bissouma to Spurs and defender Marc Cucurella to Chelsea for a combined fee of more than £90m.
Pochettino is out of work after being sacked by Paris Saint-Germain, but ESPN has previously reported that the Argentine coach would be open to a return to English football. He was considered for the Manchester United job this summer before Erik ten Hag's appointment at Old Trafford.
Zidane is also a free agent after resigning from Madrid in May last year, saying the LaLiga club lacked faith in him despite delivering three Champions League titles in a row during his first stint in charge at the Bernabeu.