Zidane shocked world football on Thursday when he confirmed in a hastily arranged news conference that he was resigning from his post just five days after guiding the club to a third successive Champions League title.
Madrid president Florentino Perez insisted Zidane's decision took him by surprise when he was informed on Wednesday, leaving him with the unenviable task of replacing a hugely successful coach.
Mauricio Pochettino, Arsene Wenger and youth team coach Guti – who used to play for the club – are said to be the leading contenders, but Sarri has also been touted as an option after he was dismissed by Napoli despite leading them to a second-place finish in Serie A.
Although Sarri still has legal wrangles to sort with Napoli and is being heavily linked with Chelsea, Reina – who is joining AC Milan in July – believes the coach's "maniacal" way of working makes him suitable for anyone.
"We are similar people," Reina told AS. "We had a father-son relationship – I love him very much and I will also be eternally grateful.
"He is the main inspiration of the records that Napoli has always been setting in these three years and he plays a great game.
"I would recommend it to any team in the world, for his football ideas and his maniacal way of working."
Reina's time in Naples will conclude when his contract expires at the end of June.
It has been a long time in the making, as the Spain international revealed he wanted to leave a year ago when Paris Saint-Germain made an approach, while he expects it will be his final transfer before retiring in Milan.
"I wanted to leave a year ago," he said. "PSG made me an offer, but Napoli rejected it.
"It would've been easy to force the exit, but the players made a pact for the Scudetto and I decided to accept the decision.
"Milan is one of the biggest clubs in the world. We have an obligation to return to the Champions League, which is an exciting challenge. I am happy to close out my career at Milan."