The Ivorian striker was alongside owner Roman Abramovich to watch last week’s win over Sunderland and has been at the club’s Cobham training ground this week.
It now appears that Abramovich wants him back on a permanent basis.
Drogba, aged 37, left Chelsea on a free transfer at the end of last season and signed a two-season deal with Montreal.
He scored 11 goals in 11 MLS games last season and the Impact are keen to keep hold of him for the second year of his contract.
The Canadian outfit took to their official Twitter account to confirm that Drogba had sought to be released from his contract and that they were currently in discussions with both him and Chelsea.
They said they were doing everything possible to keep Drogba, but said the situation was out of their control.
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