Simeone refuses to rule Costa out of Champions League final
Atletico Madrid's Argentinian coach Diego Simeone celebrates their Spanish league title at Neptuno square, in Madrid on May 18, 2014 - by Pedro Armestre
Both players were forced off with injuries inside the first 25 minutes as Atletico claimed their first La Liga title in 18 years with a 1-1 draw away to Barcelona at the weekend.
Spanish media reported on Monday that Costa will miss the final after suffering the recurrence of a hamstring problem, whilst Turan has a hip injury.
"We are just starting the week. There are still a few days to go and we are not going to jump the gun because I think it is too early for such an important game, but we need the players to be in the right condition.
"We will wait to see how Costa and Arda recover until the end of the week and we will look for alternatives if they don't recover."
Atletico go into the game full of confidence having ended Real and Barcelona's 10-year domination of La Liga and having lost just twice in 10 meetings against the two this season.
However, Simeone played down the influence winning the league could have in Lisbon.
"Winning is always good, but you have to move on straight away. We need to be 100 percent concentrated and I am sure the players will respond as they have always done in the biggest games."
Victory on Saturday would deliver the fifth trophy of a glorious two-and-a-half year spell since Simeone took over in December 2011.
And the Argentine dispelled rumours that he could leave the club at the end of the season.
"I am very happy where I am. There has been a great progression. We won the Europa League and the European Supercup then the Copa del Rey final and reached the Champions League. Now we have won La Liga and the team continues to grow.
"If we maintain a competitive team we are going to fight with the best despite the economic differences. I will stay here next year."
Both sides are likely to be weakened as Real also have doubts over the fitness of Cristiano Ronaldo and Karim Benzema.
However, Simeone believes the absence of the suspended Xabi Alonso in the Real midfield could be the biggest setback of all.
"He is one of the best, but (Carlo) Ancelotti has alternatives. Whether it be (Asier) Illarramendi, (Sami) Khedira or Casemiro. One of those three will play. It is an important loss for them for what he means as a player."