And Luis has revealed that he is glad to have him back – with the pair having won La Liga during the 2013-14 season.
“[Costa] is the best I have played with,” Luis told El Mundo.
“I have seen [Juan Carlos] Valeron do things nobody could do. Neymar and [Eden] Hazard are amazing talents, but the player who gave me most trophies was Diego Costa.
“He always scores the opening goal. Because it is one thing to score 30 goals with hat-tricks in easy wins, and another that 20 of those 30 goals are enough to win 1-0. Nobody does that as well as Diego Costa.”
Diego Costa, en su primer entrenamiento con el Atlético
Image credit: Eurosport
Luis, who also spent a year at Chelsea before returning to Spain, has backed Antoine Griezmann to stay at the club amid speculation he could join Manchester United.
“Often players talk when they feel they are not being valued as they deserve. Then they get more attention.
“He would have had many offers from many teams. A player of his size wants to be up with the biggest in terms of contract and value. And that is fair - as Griezmann is doing great here.
Antoine Griezmann, celebrando un gol ante el Chelsea en Champions, en el Metropolitano
Image credit: Getty Images
“In the end, for all the talk about other clubs, he always wanted to stay here and he is still here, happy and liking it.
“For sure, he can stay much longer. We hope the fans understand this and everything gets back to normal, although he has been scoring goals, and goals cure everything.”