Thomas Tuchel has previously worked with Dembele in Borussia Dortmund.
The Blues could make their first signing of the summer as early as next week.
Dembele’s contract with Barcelona expires by the end of this month and Chelsea are favorites in landing the French international.
Both Tuchel and Dembele could reunite at Stamford Bridge as they previously worked at Dortmund back in 2016.
He has struggled with injury troubles and disciplinary problems but talkSPORT reporter Alex Crook believes he’s close to a Chelsea move.
Crook told talkSPORT: ‘This one has really taken off overnight.
‘Chelsea look like they are favourites to sign Ousmane Dembele on a free transfer.
‘He’s been letting his contract run down at Barcelona and he would be the first signing of the Todd Boehly era.
‘How do you think that would go down with Chelsea fans?’
Even manager Thomas Tuchel has praised the French international previously when he was managing at Dortmund.
‘Of course, we love his dribbling, we love his bravery, we love his pace, his control on the ball, we know a lot of the facets of his game from the training,’ Tuchel said during his spell in charge at Dortmund.
‘Ousmane is a player who brilliantly combines dribbling, passing and making space to a very high level. That’s extraordinary.’