Reports on Tuesday suggested Real were lining up a summer swoop for Aguero, who joined Manchester City from Atletico Madrid for £38 million last summer, scoring 17 Premier League goals since the switch.
It was also claimed that Higuain could be involved in the mooted deal, with the Argentina international heading in the opposite direction.
But, speaking ahead of Wednesday's Champions League tie against APOEL Nicosia, Mourinho said: "You (the press) want to destabilise the squad.
"Last week I had signed for (Manchester) City, (Iker) Casillas was going to Schalke, Higuain to Malaga..."
Asked specifically about the Higuain-Aguero story, he added: "The front cover of (newspaper) AS is false. If you want me to comment on false front covers then forget it."
The club's director of institutional relations Emilio Butragueno also dismissed the suggestion of selling Higuain, who has been in impressive goalscoring form this season.
"Rumours seem to be inevitable," he told the club's official website. "But we are delighted with Higuain. He's scored 24 goals in 20 league games and just remember I was the league's top scorer with 19.
"He is a world-class striker and we intend for him to stay here many years. He arrived here very young and we regard him as a club player. He has always behaved impeccably, whether he plays or not."