It was reported earlier on Friday that Chelsea were close to completing a deal for the Atletico Madrid forward, but despite admitting that he rates the Spanish international, Mourinho wouldn't reveal if he wants to bring the player to Stamford Bridge.
The 51-year-old told reporters: "The transfer window is closed and it opens in the summer. Chelsea will be quiet during that period. We are not going to be the noisy team, buying and selling and selling and buying.
"We're going to do a couple of critical signings. Is a striker a target for us? Yes. We never denied that. Is Diego a good player? He is, but he is an Atletico Madrid player so we cannot say much."
Costa scored against Chelsea on Wednesday evening as the La Liga side recorded a 3-1 win at Stamford Bridge in the Champions League.