Drogba scored 11 goals in 11 appearances for Montreal last season, but is understood to be interested in returning to former club Chelsea in a coaching capacity, following the dismissal of Blues boss Jose Mourinho.
The Daily Mail is reporting interim Chelsea manager Guus Hiddink wants Drogba as part of his backroom staff, which may be enough to see the Ivorian walk out on the second year of his contract with the Impact.
Montreal released four tweets explaining to the club's fans they are doing all they can to keep Drogba in Canada.
"We understand his attachment to his former club and his desire to help them. We are willing to accommodate him. #IMFC
"But our objective is to have him back for another season, as agreed in his contract. This situation is out of our control. #IMFC
"We would like to thank our supporters for their understanding and their patience. #IMFC."