The Spaniard has been struggling with a hamstring injury for the last fortnight and Simeone said on the weekend that he would return for the second leg in Spain next week.
Hell be back for the second leg, but I dont think hell have a chance for the first, said Simeone.
However, Costa was included in Atleticos squad that travelled to London today and he could take a place on their bench for the game on Thursday.
The likes of ex-Chelsea and Liverpool man Fernando Torres is in the squad alongside star striker Antoine Griezmann.
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The game takes on added importance for Arsenal now following the news that Arsene Wenger is set to step down at the end of the season.
The Europa League is Wengers last chance to end his tenure with silverware and winning it would mean a route back into the Champions League.