The 32-year-old has been integral to the west Londoners' many successes since arriving as a relative unknown from Rennes a decade ago.
However, this season Cech has been displaced by Thibaut Courtois and has been regularly linked with a January departure from Stamford Bridge.
Arsenal, AC Milan, Roma and Real Madrid have all been mentioned as potential destinations for the Czech, but the interest of such clubs surprises Mourinho.
"Are you telling me that or asking me that?" the Chelsea manager said
"On which Mickey Mouse website? On which Mickey Mouse blog?
"At this moment, news is coming instantly
News is born every day, every minute, every second.
"Some websites, some blogs, we don't even know where we get the news.
"I promise you what I tell you is the truth
On my desk, normally from my board's desk, the information arrives
On my desk I have zero
Cech recently expressed his frustration at having dropped down the pecking order at Chelsea, telling Czech radio a move could be on the cards if he continued to be benched.
They are comments that Mourinho says the goalkeeper, reportedly available for just Â£7million, has not made to him.
"No, I believe in what is happening at this moment," the Portuguese said
"In this moment, Petr Cech is our goalkeeper and has a contract for two more years
"He's a fantastic professional, always puts himself available for the team and the team's interests.
"Not once has Petr Cech knocked on my door to inform me of his desire to accept some proposal
This is my truth
Nothing more I can say."
Source : PA