The Italian coach, whose Lazio side currently lead Serie A, made the comments in remarks collected by AS while discussing the Portuguese left-back's qualities. Gattuso has not been shy about putting the 26-year-old's name forward as a player capable of thriving at the very top of the game.
"I have always said that Nuno Tavares is a Real Madrid level player," Gattuso said. "A player of his quality could have played 10 years for Real Madrid. He should be at Real Madrid. He has it all, he has speed, right foot, left foot."
Gattuso did, however, acknowledge an unusual side to the defender's character, one that requires careful man-management.
"He's unusual, but after a game he needs his time to recover," Gattuso said. "But he's a good guy, you have to get into his head and make him understand it. He knows that he has talent and could have had 10 or 12 years at Real Madrid with his qualities. You just have to make him understand it."
Tavares joined Lazio on an initial loan from Arsenal before the move was made permanent, having previously struggled to establish himself in the Premier League following his switch from Benfica. Since arriving in Rome, the full-back has developed into one of the most reliable performers in Gattuso's side, contributing at both ends of the pitch as Lazio have made a strong start to the season.
Real Madrid strengthened their left-back position over the summer with the €55 million signing of Marc Cucurella, but Gattuso's comments are likely to fuel further speculation over Tavares' long-term future, particularly given the growing reputation he has built for himself in Serie A this season.
Tavares initially joined Lazio on loan after failing to nail down a regular spot at Arsenal, where his time in England also included a difficult loan spell at Nottingham Forest.
Since committing to the move permanently, he has become a first-choice pick under Gattuso, leading his side in several defensive and attacking metrics through the opening weeks of the campaign as Lazio have made an unbeaten start to the Serie A season.