The Manchester City striker is keen to link up with the Brazil-born attacker for the Spain national team, labelling the Atletico Madrid forward "a great player"
The Brazil-born Atletico Madrid star wants to represent the reigning world champions rather than the Selecao and the former Sevilla man is keen to team up with La Liga's current highest scorer.
"Diego Costa's a great player and you can't argue with that," Negredo told reporters.
"If he comes to the team to contribute, to strengthen and support the team then he will be welcomed with open arms.
"I like him a lot as a player. I've always wanted to have him in my team but it's up to Del Bosque to decide if he picks him."
Costa has twice lined out for Brazil but can still switch allegiances as the 25-year-old has yet not appeared in a competitive game for the Selecao.