The recently-crowned Liga champions saw Costa limp off with a hamstring problem in last weekend's title-winning 1-1 draw against Barcelona - sparking fears he could miss the final in Lisbon.
Arda Turan was also forced off with a knee injury and he too could be absent as Atletico look to complete the double with victory over fierce rivals Real Madrid.
Atletico confirmed on Monday that Costa - who sat on the Camp Nou sidelines in tears after his substitution - had suffered a grade one hamstring strain.
Simeone refused to be drawn on whether the pair would be fit for the final but said both would be given time to prove their fitness.
"We still have some days to go and I'm not going to say anything yet. It is too soon," he said.
"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."
Real have had the better of the meetings with Atletico since Simeone's men won the Copa del Rey at the Bernabeu last season.
While Costa helped Atleti to a narrow La Liga win in September, Real ended their rivals' Copa defence at the semi-final stage before a draw at the Vicente Calderon in March.
Simeone expects a performance similar to those that helped them win the league title and predicts a close encounter.
"We arrive with a major motivation and desire. It will be a close game," he added.
"On Saturday we need 100 per cent attention. I'm sure the players will respond as they have always responded."
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