Now Rodgers has revealed that a deal is all but over, before dismissing reports linking him with a move for Aly Cissokho.
"I believe Costa has signed an extension," Rodgers told reporters. "There's nothing in terms of players to add.
"We've signed players early on and we hope to sign some more before the end of the window. In the meantime, there's nothing at the minute."
He added: "There's nothing on the Cissokho story."
Liverpool are in action against Celtic this evening in a pre-season friendly.