Chelsea boss Jose Mourinho substituted Cole in the second half of the Blues' 3-1 win at Norwich and revealed afterwards that the left-back was suffering from a rib injury.
Cole - who has won 105 international caps - did not report for England duty on Monday and has been ruled out of the first of two critical qualifiers against Wembley as he requires further treatment with his club.
If not, Arsenal's in-form left-back Gibbs is a promising deputy. He has won two England caps in a career regularly interrupted by injury, but has been a key man in his club's rise to the top of the Premier League before the international break.
England top Group H by just one point thanks to their draw in Ukraine last month. The only way they will guarantee qualification is by winning their final two games.
The squad met up for the first time at St George's Park in Burton on Monday.
Hodgson will spend the next four days trying to put together a masterplan to defeat Montenegro, who held the Three Lions to a 1-1 draw in Podgorica in March.