Both teams are enduring difficult spells, with speculation mounting over Manuel Pellegrini and Rafa Benitez's future.
Mancini, who is free to join another club after terminating his Inter deal, has denied speaking with either club.
The 44-year-old is ready to get into management and has confirmed he will review any offers that come his way.
"Contact with Real Madrid and Liverpool? At the moment there has been nothing," he told Radio Rai.
"But it's clear that when there's talk about coaches of clubs in difficulty there are rumours involving the coaches who are free.
"We will see. Should something arrive, we will evaluate."