The Frenchman believes his protege has the ingredients to succeed his senior at Real Madrid and addressed comparisons with Barcelona duo Xavi and Sergio Busquets
The 48-year-old saw Illarramendi blossom after the midfielder played a crucial role in Real Sociedad's surprise qualification for the Champions League last season.
And Montanier has maintained his belief that Illarramendi's characteristics are ideal to fill Alonso's boots at the Bernabeu in the long term.
"Yes, he’s definitely ready," the Rennes boss told AS. "He has many strengths. He has enough quality to move the ball forward and link-up with other players.
"Xabi is a reference point for Basque players and I feel that he can help him [Illarramendi] to grow and develop too. They can definitely play together. Xabi and Asier are both great players.
"He [Illarramendi] is also very modest. The ideal player for any coach because he’s a nice guy, but on the pitch he gives it everything. He will be a fantastic player for [Carlo] Ancelotti because he always listens to the explanations you give him.
"He has the right character to be a success and he’ll be a big player for Spain too.”
Illarramendi has earned comparisons with Barcelona counterpart Sergio Busquets, but Montanier felt the 32 million euro signing mirrored another Catalan player.
"Comparing is always difficult. Asier has different qualities [to Busquets]; the same role, yes, but different qualities. Asier is more in the mould of Xavi," he continued.
"Not only is he a midfielder that works hard to get the ball back, but he has enough quality to be involved in getting things moving and distributing the ball.
"He’s not bothered by what’s happening around him, only what happens on the pitch, and that’s where I have faith in him."