Perez told Sky Sports News that Mourinho was going back to Stamford Bridge, six years after the Premier League club sacked him.
It is unclear on what authority Perez made the claim, as he would play no part in Mourinho's negotiations with Chelsea.
The 66-year-old Perez was re-elected Real Madrid president unopposed on Sunday.
Mourinho took charge of his final game as Real Madrid coach on Saturday, beating Osasuna 4-2.
He was given a mixed reception from the club's fans, many of whom have been critical of his abrasive style that has seen him fall out with senior players such as goalkeeper Iker Casillas.
The article, which was live for several hours early on Sunday, purported to confirm an agreement to take Mourinho back to Stamford Bridge.
The Premier League said: "It was a publishing error. We took it down as soon as we were notified of it, and we've spoken to and apologised to Chelsea. We have no prior knowledge of any movement or any announcement."
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- Real Madrid