The Premier League giants have been linked with the star Atletico Madrid striker, who has scored 27 La Liga goals this season.
Mourinho was unwilling to say whether Costa was the man his team were chasing but said a striker was much-needed.
"We are not going to be buying and selling and selling and buying," Mourinho told a news conference.
"We're going to do a couple of critical signings. Is a striker a target for us? Yes, we've never denied that.
"Diego Costa is a good player but he's an Atletico Madrid player so I cannot say much."
Mourinho gave even less in regards to the future of goalkeeper Thibaut Courtois, who is in his third season on loan at Atletico but owned by Chelsea.
"I prefer to say that he is Atletico Madrid's goalkeeper. I prefer to call him that," he said.
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