Sociedad sporting director Lorenclaimed earlier this week that there had been "indications" of interest from the capital outfit, but Aperribay has insisted that no bid has been received.
"Madrid have not enquired to us about Inigo Martinez," Aperribay told reporters.
"So I hope that it is just a rumour and that he will continue with us for next season. My desire is that no player will leave La Real because what we are trying to do is find a team and maintain a structure.
"We are very hopeful that the team can stay as it is for next season and that we can even strengthen it with new signings."
Martinez, who is now a senior Spain international, has also been linked with Barcelona.