The Atletico Madrid coach is still hoping that the 25-year-old could feature against Real Madrid on Saturday, despite picking up a hamstring injury
The Spain international lasted just 16 minutes during Saturday's 1-1 draw with Barcelona, which won his side La Liga for the first time since 1996.
The club confirmed that he had a grade one hamstring injury, Simeone is still holding out hope that the 25-year-old could yet recover in time to face his side's arch rivals this weekend.
"We still have some days to go and I'm not going to say anything yet. It is too soon," he told reporters.
"We'll wait on the injury news from Costa and Arda until the end of the week. If necessary, we'll opt for alternatives as needed.
"This is not a game for players who are at 80 per cent. Obviously, we need players who are in good condition."
Simeone has told his troops that any lapse of concentration could cost them against Carlo Ancelotti's men.
"We arrive with a major motivation and desire. It will be a close game," he added.
"On Saturday we need 100% attention. I'm sure the players will respond as they have always responded."