The 24-year-old winger scored in the Champions League final last season and has gradually emerged as one of the key players in Hansi Flick’s squad.
The Frenchman still has more than two years left on his contract with Bayern Munich, but the German champions have been keen to reward him with fresh terms.
But Coman recently rejected an offer of a new deal and is demanding more money in line with his importance in the Bayern Munich squad.
Chelsea are keeping tabs on his situation, but according to German daily Bild, the negotiations are on again between the club and the player.
The German champions remain intent on offering him a new contract and they have resumed talks with Coman.
It is unclear whether they are willing to match the kind of money the Frenchman wants on his potential new contract.
Manchester United offered Coman a bumper contract to leave Bayern Munich last summer, but he decided to stay put.
It remains to be seen whether interest from Chelsea forces Bayern Munich to offer him the kind of terms he wants.