Blues boss Antonio Conte has been busy in the transfer market this summer, but wants further additions before the closure of the transfer window, and Oxlade-Chamberlain is thought to be high on his wanted list.
The England international has just one-year remaining on his Gunners contract, but has yet to sign a new one, leading to suggestions he could be on the move, with Chelsea, Liverpool and Manchester City all interested.
Gunners boss Arsene Wenger is not concerned about the contract situation and has previously ruled out the possibility of the forward moving on this summer.
However it has now been suggested that Oxlade-Chamberlain would be open to a move to Stamford Bridge as it would mean Champions League football again next season, and a pay rise.
Chelsea have been linked with a £25million bid, but reports now claim that Conte is willing to go as high as £35million if it means getting Oxlade-Chamberlain on board.