The experienced left-back, who has 105 caps, was substituted for tactical reasons with 15 minutes remaining of the 3-1 victory at Carrow Road on Sunday.
However, it later emerged that Cole had suffered an injury and the 32-year-old is now set to undergo a scan ahead of England's crucial home games against Montenegro and Poland next week.
Chelsea manager Jose Mourinho said: "Cole goes for a scan on the ribs when we arrive back. I hope he's fine.
"I didn't know (that he was injured). It was a tactical decision. He had something in his ribs that we need to assess, but hopefully it’s fine."
Chelsea wrapped up the win following late goals from Eden Hazard and Willian, after Anthony Pilkington had cancelled out Oscar's early opener.
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