The 52-year-old former Celtic midfielder, who won the league title with the Hoops twice in the 1980s, worked with Dembele at Fulham.
The 21-year-old striker has had injury issues this season, and has also not played as well as he did during the 2016-17 campaign.
Grant, though, has compete faith in Dembele, who cost Celtic £500,000 when they secured his services from Fulham in the summer of 2016, according to The Scottish Sun.
“Moussa can have poor games like any other player but no one should question his commitment or what Celtic mean to him,” Grant told The Scottish Sun about Dembele. “He cares just as much about Celtic as he did when he joined.
“Moussa doesn’t need to be told how good the club’s been for him. He’s also aware of what being successful there could be for his career.
“Moussa’s body language has always been the same. I’ve known him long enough. He could score a hat-trick and still look no different, that supposedly couldn’t-care-less look, but that is his make-up. Moussa’s the same if he misses a chance.”
Dembele may have scored only 12 goals for Celtic this season, according to The Scottish Sun, but there is no doubt that the French striker is a brilliant player.
The former Fulham youngster will be a key player for Celtic in the Old Firm derby against Rangers away from home at Ibrox on Sunday afternoon.
If Dembele starts the Scottish Premiership game, then he could well score a goal or two.