The Blues had a bid accepted by Arsenal on Monday which will see it rise above £35m with add-ons and it is understood they moved quickly as they fear Liverpool in the background.
It now remains to be seen whether Liverpool will try and make a last-ditch bid but Chelsea know that there have been strong overtures from Anfield to try and get him.
Oxlade-Chamberlain, 24, sees his future in midfield and that might be easier at Liverpool while Chelsea are looking at him to play right wing back.
But Chelsea do appear to be in pole position despite other Arsenal players being convinced that he was angling for a move to Merseyside.
Chelsea know they cannot miss out on another transfer target as Antonio Conte has been left frustrated all summer and they appear to be deadlocked again over Danny Drinkwater.
England boss Gareth Southgate will allow Oxlade-Chamberlain to leave the training base at St George’s Park and potentially even miss the trip to Malta to resolve his future.
But Chelsea are now hoping to make quick progress and tie it up in the next 24 hours to steal a march on Liverpool.