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."
Mourinho caused controversy earlier in the campaign when he was secretly filmed questioning the aptitude of his current strikeforce, which includes the likes of Fernando Torres, Samuel Eto'o and Demba Ba.
Mourinho is confident Chelsea will be in a better shape to win trophies next term after a 'transitional' season at Stamford Bridge.
And he has also questioned Eden Hazard's team ethic in the wake of Chelsea's midweek Champions League exit.
"Eden is the kind of player that is not so mentally ready to look back to his left-back and to leave his life for him.
"If you see the first goal of Atletico you completely understand where the mistake was and why we conceded that goal.
"The perfect team at the top level cannot make these kinds of mistakes."
While Mourinho has praised Hazard's willingness to work at times this season, he says there is still a lot of work for him to do.
"I'm not happy," Mourinho said. "I speak all season and I try to improve him all season."