Cole has fallen out of favour at Stamford Bridge in recent months under Jose Mourinho, and is out of contract in the summer.
Talks have not begun over a new deal, and the Blues have been heavily linked with a number of left backs, including Southampton’s 18-year-old star Luke Shaw.
Mourinho opted for right footed Cesar Azpilicueta to start at left back against Manchester City on Monday night.
The Spaniard has started every big game this season at the expense of Cole, featuring against Arsenal (twice), Liverpool, Manchester United, and most recently at the Etihad.
With Mourinho clearly planning a future without Cole, speculation has began over where his next move will be.
And some are suggesting a shock return to Arsenal, the club he left in 2006, is in the pipeline.
Arsene Wenger refused to rule out a possible move for Cole after Arsenal’s 0-0 draw with Chelsea on December 23.
Asked whether he would be prepared to re-sign a man who forced through a move to Mourinho’s Chelsea in 2006, Wenger replied: “If I needed a left back, yes.”
Cole has added to speculation surrounding his future in recent weeks on Twitter.
First he claimed he hoped Chelsea completed a move for Luke Shaw, and then replied to a fan who had praised his performance in the FA Cup clash with Stoke by saying: “cheers mate just don’t get used to it.”