The Argentina-born striker says that Los Blancos have not lodged any bid for him, but claims that the Spanish club's director would like to see him at the Santiago Bernabeu
Italian sources have suggested that the La Liga champions were willing to offer Fernando Gago plus €10 million in a bid to sign the forward, who signed for Roma only last summer.
The former Espanyol man claims that Madrid have not yet expressed an interest in him, but revealed that Zidane thinks he would be a quality addition to Los Blancos.
"I have read the rumours about Real Madrid and their interest in me," he told ESPN. "But I have not heard anything or received any offer.
"At a recent charity event, Zinedine Zidane told me he would like to see me play for Madrid".
The 26-year-old, who cost the Giallorossi €17.5m, then spoke of his delight to have moved to the Stadio Olimpico, where he scored 11 Serie A goals this season.
"It was a huge step for me to join Roma," Osvaldo noted. "When it comes to just how I felt playing football, I found it easier in Spain.
"But I am happy that I have joined Roma and last season was a great one for me."
The Italy international, who was left out of the Azzurri's Euro 2012 squad, also shed some light into his bust-up with team-mate Erik Lamela in the wake of a Serie A match against Udinese.
"It was just the heat of the moment," he explained. "I always want my team-mates to pass me the ball because I am a No.9.
"I am egotistical, but you have to be that when you are a striker. But that incident was nothing, really.
"If I had the kind of left foot Lamela has, I would not have passed the ball there either. It was just an argument.
"It happened with Lamela, but it was nothing personal, it could have happened with Totti, too!"
Since March, Goal.com has been publishing exclusive extracts from Luca Caioli's new book, Ronaldo: The Obsession for Perfection. This Friday's excerpt looks at how Cristiano and Portugal lost out in the final of Euro 2004. Don't miss it!