"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," Costa told British media.
"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."
Hazard has been nominated for the PFA Player of the Year award and media reports have linked both players to transfers away from Chelsea at the end of the season.
"He's a boy that impresses me every day, he has a huge potential. He is a beautiful person, a humble guy," Costa said.
"We get on really well while playing and I hope we stay together like this for a very long time."
Chelsea travel to fifth-placed Manchester United on Sunday with their last three visits to Old Trafford ending in draws.
(Reporting by Aditi Prakash in Bengaluru; editing by Sudipto Ganguly)
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