The Blues have stepped up their interest in the England international over the past week, According to Sportsmail.
Arsenals are aware of Chelsea’s interest and have rebuffed initial overtures.
Chelsea will now intensify their efforts to lure him as they look to fulfill Antonio Conte’s desire to strengthen the squad before the end of transfer window.
Chamberlain has one year left on his deal, meaning he can leave at the end of the season.
The Gunners are keen to keep him beyond his existing deal, but have left themselves exposed with regards to his contract.
It leaves Arsenal facing the dilemma of losing him for nothing or listening to offers.
Chamberlain has excelled in a wing back role of late for Arsenal and would fit in perfectly to Conte’s 3-4-3 system.