Reports in England claim that the pair recently had a fallout after Costa was offered a £30m-a-year offer to move to China and the argument allegedly ended in Conte telling the striker to "go to China".
Costa was left out of the Chelsea squad to face Leicester at the weekend, but is thought to be in contention to face Hull on Sunday.
Former Chelsea striker Hasselbaink believes that the Spain international will have no problems at Samford Bridge as long as he keeps scoring goals.
"I think only Costa can keep Costa happy, I don't think Chelsea are going to keep him happy.
"He's playing the best football of his career, of course he's going to get other clubs interested, it's just the nature of the game, and Chelsea will have to deal with that.
"It's how he takes it further. He might want to leave, but if he keeps on doing the business on Saturday there's no problem there.
"The team is the most important thing, and Chelsea need to do the right thing for Chelsea. The boy is under contract and we all know Costa is a very important player in the Chelsea set-up, especially in counter-attacking, bullying and leading the front line".
Costa is Chelsea's top goalscorer this season with 14 goals in 19 Premier League games.