The Portuguese, who was sacked by Manchester United in December, has been linked with a return to the Liga giants in the wake of their shock Champions League exit to Ajax on Tuesday.
Merengues supporters sang the name of their former coach, who led the club from 2010-13, outside the Bernabeu after the 5-3 aggregate defeat.
“The chants? I am proud, but Real Madrid have a coach,” Mourinho told El Chiringuito TV.
“Obviously I am proud when you hear your name in that context, but there's nothing more than that because there has been nothing, not even the minimum contact.
“I haven't spoken to anyone and there are a lot of rumours, but we all know that rumours in football are not good and they are not strong.
“The result was surprising when you see what this club has done recently in this tournament; winning four out of five Champions League is incredible.
“They know that when they have those victories I'm happy for them, and they know too that I'm not happy about what happened at the end of my spell.
“I have a lot of respect for what they've done because I don't think it will be repeated.”
