The Real Madrid president has branded Kaka a "phenomenon" and has high hopes that Carlo Ancelotti can bring the Spanish club the long-awaited Decima
The Portugal forward, 28, is yet to sign extend his contract beyond 2015 with the club, triggering suggestions that he might depart this summer for Manchester United or, more recently, Monaco.
The lack of a new deal does not bother the Spanish club's chief, however, who insists that the attacker has a huge future with the club.
"He is the face of the team and the best player in the world," he told Gol Caracol on Friday. "He is going to give us much more satisfaction for his talent, ambition and enthusiasm; and now he has reached a perfect relationship with the fans.
"We are yet to see the best of him. He can be the best of all time."
Perez is also keen to see Kaka, who has been linked with a move away in recent transfer windows, return to his best at the Santiago Bernabeu, and he remains confident that the Brazil international can rediscover his Ballon d'Or-winning form.
He added: "He is a phenomenon. He was injured after the  World Cup and had surgery on his knee and then [Mesut] Ozil came and took place. But he is one of the greats.
"On Twitter, after Cristiano, he has the most followers [of any footballer]. He has charm and thrills the fans. I am optimistic that under Carlo Ancelotti, who knows him well [from AC Milan], he will go back to being the magical Kaka from when we first signed him."
With the arrival of Ancelotti from Paris Saint-Germain, Perez is hoping the club can finally claim the elusive 10th top European trophy this coming campaign.
"This season will begin a new phase following the departure of Jose Mourinho," he said. "We have another coach, who is also very demanding and we are very happy.
"Our signings are young and hungry, which is necessary so that the big players don’t always get too comfortable. And the mix will make the quality of Real Madrid prevail over everyone.
"We will see if we will win the Decima, which continues to elude us. Because, as the first winners of the tournament, it is something we have deep within our DNA; it is a competition in which we thrive.
"The Champions League nights are magical for the atmosphere and excitement they generate. And to win the title you have to be lucky, which we were not in the last two season. Madrid have to be able to beat everyone.
"We must not forget about La Liga, though. We have to play well, even when we win by a lot, because otherwise you hear whispers in the Bernabeu. The fans are very loyal, but blow cold or hot. They are very demanding."