Costa is wanted by Chinese Super League side Tianjin Quanjian, as well as Atletico Madrid.
The Spain international admitted earlier in the week that he doesn't enjoy living in London, but planned to see out the two years remaining on his contract.
Hazard's future at Chelsea is also under scrutiny with Real Madrid wanting to make him the first £100m player this summer.
But Costa admits he thrives playing alongside Hazard in Antonio Conte's 3-4-3 formation and wants to continue being his teammate.
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Costa said: "Playing with Eden is something beautiful. You're playing on the field and at the same time enjoying what he does because he is a top player.
"At every moment I know when he is going to pass the ball to me and I also know when he wants the ball from me to complete the move.
"He's a boy that impresses me every day, he has a huge potential. He is a beautiful person, a humble guy.
"We get on really well while playing and I hope we stay together like this for a very long time."