Cole to miss final qualifier
The left-back sat out Friday's win over Montenegro after picking up the injury during Chelsea's victory at Norwich last weekend.
Roy Hodgson had hoped he would recover in time for the must-win showdown with Poland at Wembley on Tuesday, but Cole will play no part after failing a fitness test.
Leighton Baines filled in for Cole against Montenegro and will retain his starting place.
Hodgson also has problems at right-back as Kyle Walker must serve a one-match suspension after picking up his second booking of the campaign on Friday.
Manchester United pair Phil Jones and Chris Smalling are the likely options to replace Walker, while Andros Townsend is expected to keep Jack Wilshere out of the starting line-up after his sparkling debut against Montenegro.
United midfielder Tom Cleverley left the squad last week after suffering a calf injury, and his replacement Raheem Sterling is set to provide cover on the bench.