It was initially claimed that Costa had 'no chance' of appearing in the match, but he has travelled with the squad and could be fit to play after overcoming a hamstring injury.
"Both in England and in Spain, many teams have suffered at the hands of Diego Costa," Simeone said. "Not just Arsenal. He has improved.
"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.
"We’ll weigh up all the various factors. We’ll speak with footballer, speak with the medical team.
"Knowing Diego Costa, I think all of those apply to him," he said when asked if Costa had come to cheer on the team or intimidate Arsenal.
"We are all very determined and motivated for this Europa League semi-final. We know we will be up against a tough team who will cause us problems and Arsenal will demand us to be at our best."