The Argentine says the striker and winger Arda Turan have "trained well" but he will make no final decision on either player until the last possible moment
The Spain international striker pulled up during his side's 1-1 La Liga draw with Barcelona last weekend after suffering a hamstring strain, throwing his participation in Saturday's clash in Lisbon into doubt.
However, both Costa and Arda - who took a heavy knock in the game at Camp Nou - trained on Thursday ahead of the game and Simeone says he will give them as long as possible to prove their fitness.
"We will examine Diego Costa and the other injury doubts today. They trained better yesterday but we have to see how they feel," he told reporters at a press conference on Friday.
"Costa and Arda are important players but they are just names, it will either be them playing or two others who know who they are. We don't know how Madrid will play, we've worked with different possibilities and we will try to block them and find a way to control the match the way we need."
Simeone admits he feels the burden of responsibility ahead of the final clash having guiding Atleti to their first league title since 1996 this season, but he insists his players have gone "above the level of mere athletes" in the past two years as they close in on an historic double.
"These players have impressed us in the last two years with their efforts. I cannot thank them enough, they have managed to represent what me and the coaching team feel for the game - passion, unity, devotion - which takes them above the level of mere athletes," he said.
"In terms of motivation, outside pressures make it easier to focus. We have to ignore those factors when we play, though.
"I don't feel as overwhelmed as people seem to think but I feel the weight of responsiblity on my shoulders. We are a compact team, a well-structured team, who are good at assessing individual situations within a match and that is why we are here.
"You can dominate the game through space, through counters - you can analyse the game the way you want and nobody holds the ultimate truth, that is why it is such a great sport."