The former Celtic star and current Fulham coach believes Dembele can reach the standard of past attacking heroes if he improves his strike rate.
Former Celtic midfielder Peter Grant has told the Scottish Sun that new signing Moussa Dembele has to aspire to emulate such former heroes as Frank McAvennie and Brian McClair, but stressed that the teenager must become more prolific in front of goal.
Dembele became the first signing of the Brendan Rodgers era at Parkhead when he joined from Fulham earlier this week, and the 19-yer-old has already shown enough potential to get Bhoys fans seriously excited.
The French starlet hit 17 goals in 46 appearances in all competitions for Fulham last season as he struck up a deadly partnership with the club's top scorer Ross McCormack, form which saw him named London Football League player of the year.
Hoops fans will be hoping that Dembele can replicate that achievement alongside 40-goal sensation Leigh Griffiths next season, and Grant believes he has the potential to do just that.
However, the man who saw plenty of the prodigy thanks to his position as academy manager says that Dembele must work on improving his strike rate in front of goal if he is to become the club's latest terrace hero.
Grant told the Scottish Sun: "He did well for us in the Championship last season, scoring 17 goals in total, and that underlined his potential. Moussa's got pace and power. But he's still raw and he has to work on being consistent with his finishing.
"Moussa at the moment is probably averaging a goal with every six chances and I told him often enough he has to work on improving that ratio. He's definitely got it in him to do so.
"Celtic have a history of brilliant strikers, guys who were prolific - in my time alone there were the likes of Frank McAvennie, Andy Walker, Charlie Nicholas, Mo Johnston, Brian McClair. Now they've got Leigh Griffiths and his 40-goal return last season was phenomenal. That's the standard Moussa's got to aim for."
The signing of Dembele, which it is alleged will only cost the club £500,000 in compensation, is undoubtedly a huge coup with several high-profile English and European clubs thought to have been chasing his signature.
Celtic will be hoping that the talented youngster's success in the Championship translates well into life in Glasgow as they look to hold off the challenge of a returning Rangers to maintain their dominance over Scottish football.