Speculation that initially surfaced on Friday morning suggested that the Blues had already completed a deal to bring Atletico Madrid's £32 million-rated star striker to West London, just days after his penalty helped to knock them out of the Champions League at the semi-final stage.
And while Mourinho was quick to confirm that Chelsea will complete a couple of important signings this summer and went as far as to acknowledge that Costa was indeed one of their transfer targets, he stopped short of going into further detail out of apparent respect for Atletico.
"‘The market is closed. It opens in the summer. Chelsea will be calm and quiet during that period, we are not going to be the noisy team buying and selling and selling and buying.
"‘We are going to do a couple of critical signings. Is he [Costa] 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," he said.
While it remains unclear if Chelsea have put a concrete deal in place to bring Costa to Stamford Bridge at the end of the season, there is certainly no doubt that the club are in need of strengthening in the final third.
Samuel Eto'o - who has proved nothing more than adequate during his one-season spell at the club - is out of contract this summer, while it seems increasingly unlikely that either Demba Ba or Fernando Torres will be handed a stay of execution.
If indeed all three of those players were to depart the club, Mourinho would obviously need to secure replacements and it has even been claimed that they could also be looking to entice Bayern Munich's Mario Mandzukic in addition to the in-form Costa.