Atletico Madrid and Spain striker Costa was the architect of the Blues' Champions League semi-final exit earlier in the week and rumours suggest Mourinho is keen to add the 25-year-old to his squad for next season.
But while Mourinho confirmed his interest in bringing at least one top-class striker to Stamford Bridge during the summer transfer window, he stopped short of discussing any specific targets.
The Portuguese said: "The only thing I can see is that the market is closed. It opens as you know in the summer.
"Chelsea will be quite calm and quiet during that period. They won't be the noisy team selling and buying, buying and selling. We aren't going to be that kind of club.
"We are going to do, I would say, a couple of critical signings. Is a striker a target for us? Yes. Is Diego (Costa) a good player? Yes, he is but he's an Atletico Madrid player so I cannot say much."