Sheen was fired midway through Season 7 because of his erratic behavior and drug use.
The show's producers have not yet announced whether "Men" will return for Season 8 without Sheen.
Deadline said CBS Corp. President and Chief Executive Officer Les Moonves and CBS Entertainment President Nina Tassler first approached Grant a couple of weeks ago about joining the show. Although he initially seemed interested, the actor ultimately declined, the report said.
"It was not the money. He didn't want to do TV because those 24 episodes are a grind and a lot of work. At the end he couldn't get his head around doing a series," a source with knowledge of the talks told Deadline.
Grant is best known for his work in London-set big-screen romantic comedies such as "Four Weddings and a Funeral," "Bridget Jones's Diary" and "Love Actually."