It was initially thought that Costa was definitely out of the contest, but Simeone has said that he will leave it until the last minute before making a decision.
"This is only the start of the week and there are still a few days to go until the final. We're not going to get ahead of ourselves and say anything – I think it's far too early to do something like that ahead of such an important game," he told reporters at a press conference.
"Having said that, we need all of our players in the best conditions possible. We're only concerned about ourselves. We will wait and see how Diego and Arda [Turan] progress - we'll assess them again at the end of the week and consider what alternatives are open to us if they fail to recover."
Costa has scored 36 times this season.