The Brazil-born attacker is eagerly anticipating Saturday's top-of-the-table clash with Barcelona and is adamant that his side do not fear the Argentine forward
The Argentina international returned to match action after a two-month injury lay-off by scoring a double in Barcelona's Copa del Rey win over Getafe on Wednesday.
Nevertheless, Costa insists that Atleti do not fear Messi as he is confident that his side's defence are up to the task of nullifying the 26-year-old's threat.
"Messi is Messi. We all missed him while he was out. It'll be nice to have him up against us. He'll be up for it after being out for so long," the striker told AS.
"But we will be making it difficult for him; we have players at the back who are capable of stopping him.
"It's going to be a difficult game against an opponent who have some of the world's best players but we are at home and we can make life difficult for them."
Atletico and Barcelona currently sit joint-top of La Liga with 49 points from 18 games.