The experienced centre-back is thought to be assessing his options, with a view to a move away from Stamford Bridge in the winter, having struggled for game time under Maurizio Sarri so far this season.
Now 32, Cahill is out of contract at the end of the season and is keen to be playing regular football at this stage of his career.
The heart of defence continues to be a concern for Manuel Pellegerini's side, who have kept just a single clean sheet in eight Premier Legaue games so far this season.
With 61 England caps and almost 350 Premier Legaue appearances to his name, there are few players more experienced that Cahill on the market and with the Dronefield-born battler having player just 201 minutes of football so far this campaign, he could well be tempted to join the project at the London Stadium.