The Canadian Press learned that negotiations between the club, Drogba’s representatives and MLS began about 10 days ago.
The spokesman also confirmed that Saputo talked with the former Ivory Coast international last Friday and that discussions happened in French – Drogba’s native language.
The Chicago Fire are also in talks with Drogba and his name is on their discovery list.
That gives the Fire exclusive rights to Drogba should he decide to join MLS.
Montreal could still sign Drogba, but it would need to pay a fee to Chicago to acquire his rights.
If the negotiations fall through between the Fire and Drogba, the MLS would likely ask the Fire to waive their rights on the 37-year-old to allow him to sign elsewhere.
Montreal would be the most likely destination, as it’s the only French-speaking market in MLS.