Terry has been a proud and committed England skipper but some of the off-field stories about the Chelsea captain have concerned the hierarchy.
It will be Capello's decision whether Terry keeps the armband but some influential figures think it should be taken off him.
The subject is likely to be discussed at the next board meeting on December 19.
One member of the board said: "Nobody doubts John's ability and his desire when he plays for England but he has to understand the responsibilities which go with a very important job."
