Costa has scored 10 times in eight La Liga matches this season and is one of the in-form strikers in world football in the early part of the season.
He has twice played for Brazil – the county of his birth – in friendlies, but he wants to switch his allegiance to the Spanish national team.
"Diego Costa's a great player and you can't argue with that," Negredo told reporters at a press conference.
"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 [coach Vicente] del Bosque to decide if he picks him."
Negredo is expected to lead the line when Spain face Georgia in their World Cup qualifier on Tuesday.