The 23-year-old says any player in the world would be happy to be linked with the Club.
Reports suggest Rafa Benitez's men have identified Mustafi as a potential replacement for Sergio Ramos, who is being linked with a move to Manchester United.
"Right now I'm on vacation but who wouldn't be happy when Real Madrid are interested in you?" Mustafi responded when questioned by Sport1 about the transfer rumours.
"It proves that I've given a good level of performances this last season. No player would not be cheerful at such links."
Mustafi's father added fuel to the speculation by lauding the size and ambition of Madrid.
"It is true, there was a phone call from the club about their interest," Kujtim Mustafi said. "Madrid are a great club with a superb history of success."
"Of course, I would be lying if I said I was not proud at the thought of my son signing for this club."
Mustafi cost Valencia €8 million 12 months ago, signing a contract until 2019, and is believed to have a €50m release clause.