Lukaku currently leads the Premier League's goalscoring charts with 24 strikes this term, seven more than Chelsea striker Costa who has only scored three times in the top-flight since the turn of the year.
Such has been Lukaku's form this season that Standard Sport understands the 23-year-old has become Antonio Conte's first-choice target for a striker this summer.
With Everton boss Ronald Koeman recently admitting the Belgian star has told him he will not sign a new contract at Goodison Park, Hasselbaink believes a move back to Stamford Bridge would see Lukaku become one of the best forwards in the world.
"He's been to West Brom on loan and he's been at Everton and he's done exceptionally well. Exceptional," Hasselbaink told Premier League Daily.
"Everton paid, at the time, a lot of money for him but because he has developed that well, nowadays for players of his stature, you pay that kind of money, and if you want to have a goalscorer in your team at 24-years-old [sic] you have to pay.
"I think he has matured that's for sure, but if you compare Costa and Lukaku they're very similar. If you compare him to [Harry] Kane they are totally different.
"The way that Chelsea are playing, he is, along with [Alvaro] Morata, the player you are going to look at to take over from Costa.
"Is he [Lukaku] as good as Costa? I think they are very close. They are very similar, he's not as temperamental but he does lead the line and I think he is still going to become better.
"With all due respect to Everton, if he does go to Chelsea he will play with better players, so he is going to get better as well.
"Yes the pressure is going to be on him, the shirt will be heavier and only certain kinds of players can handle that and he will have to show that he can."