The ex-Blues striker said interest in Costa from other clubs was an inevitable result of his success at the club but said he believed the Brazilian-born Spain star would not leave the Premier League leaders just yet, despite casting doubt over his long-term future at the club.
The interview with the Dutch favourite comes following speculation over Costa's future, with the striker being linked with a big-money move to China.
Hasselbaink, who scored 88 goals in four seasons for Chelsea, remains certain the 28-year-old was staying put at the west London club.
He told talkSPORT: “You know how it is – when a striker is doing well, is doing the business and is as important as Costa, you know he is going to get some kind of interest from other clubs.
Jimmy Floyd Hasselbaink believes Diego Costa will see out the rest of the season
Pedro: This is what Diego Costa is like in Chelsea training
Chelsea star reveals how the players reacted to Diego Costa's bust-…
Let’s just concentrate on the team, on how well they’re doing with Costa, instead of talking about him leaving. He’s going nowhere
Jimmy Floyd Hasselbaink
“It’s up to him if he wants to stay or not, but Chelsea can’t afford to lose him in this moment.
“To play without him for the odd game, yes they can cope, but not five or six games in a row."
According to reports, Costa's reported move to the Chinese Super League fell through following new rules restricting the number of non-nationals in the league.
“It’s very important for him to stay at Chelsea and I think he always wanted to stay, he was just playing the market," Hasselbaink continued.
Chelsea fans react to Diego Costa comeback
Sun, January 22, 2017
Click through the gallery for the best reactions as Diego Costa returns for Chelsea
1 of 6
Click through the gallery for the best reactions to Diego Costa's Chelsea comeback
Diego Costa has been linked with a move to China
“If he keeps doing the business he can do what he wants. If he keeps scoring goals then the Chelsea fans will love him and he’ll be a hero, but he will also be at the top of the market as well – that’s just how it works.
“But let’s just concentrate on the team, on how well they’re doing with Costa, instead of talking about him leaving. He’s going nowhere.”
The comments come after Costa scored on his return to the first team on Sunday in a 2-0 win over Hull City.
Chelsea manager Antonio Conte is understood to be uncertain unsure as to whether the former Atletico Madrid striker will be offered a new deal at Stamford Bridge, with his current deal set to expire in 2019.