Cole was forced off in the second-half of Chelsea's 3-1 win at Norwich City with a rib injury.
Chelsea boss Jose Mourinho is confident that Cole will be fine for England, but Roy Hodgson is now awaiting the results of scans on the 32-year-old.
"He had something in his ribs that we need to assess, but hopefully it's fine," said Mourinho.
"He goes for a scan now, when we arrive (back in London), on his ribs. I hope he is fine.
"I want England to do (well), so I hope he's fine."
The squad will meet up for the first time at St George's Park in Burton on Monday ahead of their clash with Montenegro on Friday.
Hodgson looks to have a near full strength squad at his disposal for the games and if Cole does make it, Arsenal winger Theo Walcott - who is out with a stomach problem - is the only likely absentee from his strongest starting XI.