Reports in the English media have suggested that the Premier League club are close to tying up a £35 million deal for Costa, who was among the goalscorers as Atletico beat Chelsea 3-1 in the UEFA Champions League semi-finals on Wednesday.
Costa has become one of Europe's hottest properties this season, with his 36 goals in all competitions firing Atletico to the brink of a La Liga and Champions League double.
But while admitting he will look to make a "couple of critical signings", including a forward, in the close-season, Chelsea boss Mourinho refused to confirm whether Costa is a target when asked on Friday.
"The only thing I can say is that the market is closed, it opens in the summer," the Portuguese said.
"Chelsea will be quiet and calm during that period. We are not going to be the noisy team buying and selling, we are not going to be that kind of club.
"We are going to do a couple of critical signings, is a striker a target for us? Yes, we never deny that. Is Diego a good player? He is, but he's an Atletico player."
Chelsea's current group of strikers - Samuel Eto'o, Fernando Torres and Demba Ba - have scored just 18 Premier League goals between them this term.
