Blues boss Jose Mourinho revealed the defender requires a scan prompting fears that he could miss the vital run-in.
England play Montenegro this Friday at Wembley, before the visit of Poland next Monday.
“Cole goes for a scan on the ribs when we arrive back, I hope he’s fine,” Chelsea boss Mourinho said yesterday.
Mourinho withdrew Cole – who has 105 caps for England – after 75 minutes at Carrow Road, yet said afterwards that the substitution had been for tactical reasons.
“I didn’t know [he was injured]. We were in a difficult position before. He had something in his ribs that we need to assess, but hopefully it’s fine,” Mourinho said, adding that he will be at Wembley on Friday hoping for a home win.
England lead Group H, yet are only one point ahead of both Ukraine and Montenegro.
Should Cole miss out, England boss Roy Hodgson is likely to play Everton’s Leighton Baines, while Arsenal’s Kieran Gibbs has impressed this season and may be called up to the squad as cover.
Montenegro are hoping that key forwards Mirko Vucinic and Stevan Jovetic recover from injury. Both missed their games for Juventus and Manchester City respectively over the weekend.