In what is one of the most eagerly anticipated games of the season in Spain, La Liga's top two meet separated only by goal difference.
The fixture also sees two of the league's leading attacking threats meet with Costa, who has 19 Liga goals in 2013-14, facing Messi.
Messi marked his return from a hamstring injury with a late brace in Barca's 4-0 Copa del Rey win over Getafe on Wednesday during a 26-minute second-half cameo, but Costa is confident Atletico's defence can keep him quiet.
"I saw the goals (against Getafe), not the game. Messi is Messi. We've all missed him playing because he's Messi, it will be nice to have him in the Calderon," Costa said.
"I hope it's not his day but we know he'll be up for it as he's been out for so long. But we've got people who can stop him."
Atletico coach Diego Simeone could be boosted by the anticipated return of defender Diego Godin for the clash that would see the winners move three points clear at the summit.
Costa does not feel, however, that the result will ultimately decide where the La Liga title goes this season.
"I think it is not a decisive match, there is a lot ahead and nothing is decided," he added.
"Barcelona is a very strong team and very prestigious but the important thing is to go game by game and bring out the best in every game."
