Dembele will be out of contract at the end of this month and Barcelona’s attempts to rekindle negotiations over a new deal have not led to anything.
He is expected to move on from the Nou Camp this summer and Paris Saint-Germain and Chelsea are the two clubs fighting in the race to sign the French winger.
And according to Italian broadcaster Sportitalia, Chelsea have their nose ahead in the race to sign the winger this summer.
No agreement is still in place between Dembele and Chelsea but the negotiations are under way.
Chelsea have made progress in talks with the Frenchman’s representatives over the terms of a contract.
The Blues are prepared to offer him a four-year deal to move to Stamford Bridge this summer on a free transfer.
Paris Saint-Germain are still in the race but for the moment, Chelsea are the favourites to sign the Frenchman.
Thomas Tuchel managed Dembele at Dortmund and is keen to reunite with the player at Stamford Bridge.