The former Sevilla striker is keen to link up with the Brazil-born attacker, labelling the Atletico Madrid ace 'a great player'
The Brazil-born attacker recently revealed that he wants to represent the reigning world champions rather than the Selecao and Negredo is keen to team up with the current La Liga topscorer.
"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."
Atletico Madrid forward Costa has twice lined out for Brazil but can still switch allegiances as the 25-year-old has not appeared in a competitive game for the Selecao as of yet.