Costa has been unavailable for the first half of the season following his signing from Chelsea due to Atletico's transfer ban and now Simeone says he would like to see him in partnership with Griezmann.
"We have worked hard to bring Griezmann and Costa and hopefully we keep him for a period," said Simeone.
He was speaking after Atletico's 3-2 friendly victory over Al Ahly in Egypt, and claimed he was unaware if Griezmann was trying to negotiate his departure.
Simeone praised Kevin Gameiro who hit all three goals for Atletico.
"He always creates chances and hopefully this will give him confidence especially now that he has more competition," stated the Argentine.
"It was a complete performance from us in both halves."