Costa was subbed off with a hamstring injury in Atleticos quarter-final against Sporting Lisbon on April 12 and hasnt featured since for the La Liga side since.
The doctors will inform us but I think it wont be possible for him to be ready for Thursdays game, said Simeone.
He will be [available] for sure in the return leg, but I think he has no chance to be [fit] for the first leg game.
The 29-year-old striker has bagged six goals in 18 appearances since his return to the club from Chelsea, and Arsenal will be pleased the dangerous striker isnt available for selection.
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However, Antoine Griezmann will be ready to face the Gunners, and hes scored 26 times this season so will pose plenty of problems for the Arsenal defence.
Arsene Wengers side beat West Ham 4-1 on Sunday in preparation for the European clash with Alexandre Lacazette bagging two goals.