Odriozola is aware of the interest, but refuses to encourage it.
"It bothers me that people continue talking about Real Madrid because it is written by people who don't know me," he told Noticias de Gipuzkoa.
"You can have your preferences but I'm 100 percent Real.
"So yes, the other speculation does bother me sometimes because the interest of some of those clubs crops up and people then think you may be a fan of that team but that isn't the case.
"I know I was on the cover of MARCA but I don't think that's good. It may show that I'm working hard but I can only be focused on La Real, which is my club, where I'm very happy, where I feel very, very loved and am focused on having a great season."
He added: "Winning a title here, with the club you love, who you give everything for, who you have been watching for so long... perhaps the Copa del Rey or Europa League, would make me really, really happy.
"That would be my dream."