The England international has been struggling with the problem for a few weeks and will reportedly not play against Fulham on Monday in a bid to be fit for the Blues' FA Cup semi-final against Tottenham.
The 31-year-old did not play in the 2-1 win over Wigan at the weekend and has been receiving treatment on his ankle in the past 48 hours.
The fear is that the injury could keep the full-back out for several weeks and therefore rule him out of the crucial games as Roberto Di Matteo's side chase glory in both Cup competitions and fourth place in the Premier League.
Youngster Ryan Bertrand is set to deputise for Cole at Craven Cottage on Monday and he could also be the man to step in at Wembley against Spurs and then in the eagerly-awaited showdown with Barca.
Di Matteo also has injury concerns over other senior players at the minute with Frank Lampard, John Terry and Ramires and all will be given late fitness tests before Monday's clash while Michael Essien is still struggling to be fit as well.