The Spanish champions played a direct style of football at times last season, with Costa at the forefront of their success in the final third.
However, Simeone has insisted that his new attacking options will "maintain the same style of play".
"The structure of the team won't change. The aims and the aggressiveness will be the same because it's the basis of the side," he told reporters at a press conference.
"It gives us the stability to maintain the same style of play. The way [Mario] Mandzukic plays isn't the same and [Antoine] Griezmann could be similar. [Raul] Jimenez is in between.
"He's the most similar without being the same as Costa, but he can also play as a second striker. Whoever makes us feel the most comfortable will be who plays."
Atletico face Real Madrid in the first leg of the Spanish Super Cup tomorrow evening.