Costa revealed that the addition of Turan to the Chelsea team would make his job easier and that he enjoyed great synergy with the Turkish international and Filipe Luis.
“I would really like to be reunited with him [Arda Turan] it would be fantastic because he is a player that makes my job easier,” Costa said.
“Arda, Filipe Luis and I achieved great success together and he really is a great guy.”
Costa and Turan were part of the Atleti side that won the 2013-14 La Liga title for the first time since 1996.
The Spanish international striker joined Chelsea last summer and won the Premier League title in his first league campaign in England.
Filipe Luis also joined the Blues last summer as did goalkeeper Thibaut Courtois.
Turan would become the fourth member of the La Liga winning Atleti side to join the London-based club should he join over the next few days.
The bearded winger will be leaving Atleti over the summer and is expected to join a Premier League side.