Abraham signed a new five-year deal with Chelsea before going out on loan at Swansea, working with former Blues assistant Paul Clement and Makelele.
The 20-year-old scored 26 goals in all competitions last year during his season-long spell at Bristol City.
"He has great quality but he needs to work. He is young and has time on his side, he wants to be one of the best strikers in the Premier League. He gets an example in the way Drogba and Eto'o play. But to do that he must work like they did," Makelele told the Evening Standard.
"Can he play for Chelsea? I hope so. He needs to be successful with Swansea first and learn more and more to come back and push for Antonio Conte's team. It is going to be difficult. He needs to adapt very well but we will push him. He has to show the ambitions to reach the top.
"I tell him to do everything - run, fight. Some young players think about dribbling but they need to understand about their team mates. He is fast. Go in space and you'll make the difference for your teammates.
"It all depends on him. He's good but he has to push himself and learn more, then he can be one of the best strikers in the Premier League."
Abraham has scored three goals in nine appearances for the Swans.