Former Chelsea striker Costa scored three times in six games against the Gunners during his time at Stamford Bridge, including the equaliser in last season's FA Cup final which Arsenal went on to win 2-1.
The Spain international always seemed to be able to rile the Arsenal defence and was directly involved in red cards issued to Gabriel and Per Mertesacker during separate clashes between the teams.
He left Chelsea under a cloud after a spat with Antonio Conte as he returned to Atletico in time to be registered in the January transfer window.
Since then the 29-year-old has scored six goals but has sat out the last three matches with a hamstring problem, with Simeone claiming at the weekend the forward had "no chance" of playing in the first leg at the Emirates Stadium.
However, Costa has travelled with the remainder of his team-mates and Simeone revealed there are several reasons to be cheerful for having him available.
Asked if Costa was included to intimidate Arsenal or give his team-mates a boost, Simeone replied: "Knowing Diego Costa, I think all of those apply to him.
"Both in England and in Spain, many teams have suffered at the hands of Diego Costa. Not just Arsenal.
"He trained hard on Tuesday and he trained on Wednesday and based on what we will see fit, he will either play from the start or from the bench."
Pushed on whether Costa could be fit enough to start the semi-final, Simeone said he would be picking his side for the best available outcome, rather than to include the ex-Chelsea favourite.
"We'll weigh up all the various factors," he added.
"We'll speak with the footballer, speak with the medical team. I'll look to help the team in the best way possible and that's what I'll do. I won't try to make Diego happy."