With Loic Remy just coming back from injury and Andre-Pierre Gignac recovering from a broken foot, the 21-year-old has started five of Marseille's last six games in all competitions.
He has scored four goals in 13 league appearances so far this term, compared to three in 34 games last season.
Ayew had third-placed Marseille's best chances on Wednesday but could do nothing to avoid a 4-1 home defeat by Lyon, who claimed top spot in Ligue 1 thanks to three goals from France's Gomis.
"He has been improving and has a bright future," Baup told a news conference ahead of the Ghanaian starting at Brest on Sunday.
"I said to myself we can compare him with Gomis, who I knew at the same age," added Baup, who coached the Lyon forward at Saint-Etienne from 2004 to 2006.
"When I see what Jordan has done, I come to the conclusion they have the same abilities."
Jordan's brother Andre also plays for Marseille on the wing. The duo are sons of Ghana great Abedi Pele.
The 27-year-old Gomis, who has 10 caps for France, has been one of the most prolific strikers for years in the French league, scoring at least 10 goals each season since 2006.
