The manager of the French strugglers, Frederic Hantz, admits the 32-year-old could be an option to replace Casimir Ninga who is out with a serious knee injury.
"As Ninga is sidelined, it seems to me to a good idea to bring in a top striker to improve our results," Hantz said.
"If it's Adebayor, I'll do my best to make him as good as possible."
However, Montpellier president Louis Nicollin has indicated that his club are not in the market for an expensive new signing.
"We have already spent enough money this year and we're not too keen to spend more," Nicollin said.
Adebayor is set to represent Togo at the 2017 African Cup of Nations in Gabon which kicks off on January 14.