The 23-year-old striker has lost his place in the starting eleven under Thomas Tuchel and there are question marks over his future at the club.
With Chelsea expected to be in the market for a top striker in the summer, Abraham could have a decision to make on his future in the coming months.
And Duberry stressed that the forward has a battle ahead of him if he wants to stay at Chelsea, but conceded that not everyone can be a Mason Mount and become a mainstay in the first team.
He stressed that he will have to move on from Chelsea if he does not force his way into the team on a regular basis.
“Tammy will have to battle to establish himself”, Duberry told The Athletic.
“I’m sure he wants to be a star, the Didier Drogba of the team.
“I’m sure all of them want to have Mason’s tag as a mainstay of the team, but they have to fight with everyone else.
“If he doesn’t make it Tammy will move on, and if there’s a youngster in the academy who’s scoring goals they might try to put him in.
“But most of the time they need ready-made [talent].”
Abraham has 30 goals in 80 appearances for Chelsea but has not made the squad in their last four league games.
