Cole has been struggling with the problem that he picked up in Chelsea’s 4-1 defeat to Atletico Madrid in the Uefa Super Cup, and missed England’s 5-0 win over Moldova on Friday.
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Leighton Baines deputised for Cole at left-back against Moldova, and scored his first international goal, and England's fifth of the game, from a free-kick.
John Terry, meanwhile, is a doubt for the clash with Ukraine at Wembley.
The Chelsea captain is receiving treatment for his own ankle injury that he picked up against the Moldovans.
Terry limped through the final 20 minutes of the game in central midfield as manager Roy Hodgson had used all three substitutes.
However, speaking after the game the England manager was optimistic about his prospects claiming the injury was not long-term.