Antonio Conte will leave his post as Italy boss to take charge of Chelsea after Euro 2016 and Montella believes Ranieri would be the ideal successor after masterminding Leicester City's stunning Premier League title triumph.
"If they called me I would think, and I would spend two sleepless nights," Montella told Corriere dello Sport over the prospect of the Italian Football Federation making an approach to him.
"I think for that role, experience is fundamental. On the Azzurri bench I'd see see Claudio Ranieri doing well.
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"He is a balanced man who has experienced so much in football and proved, not just this year, his quality.
"You know how it is in our job, surprises can come at any moment. For now I see myself at Sampdoria."
Montella, who stepped in as caretaker boss at Roma after Ranieri resigned in February 2011, reflected on the emotional experience of representing Italy 20 times as a player – something he still feels to an extent as a fan.
"It is the maximum for a player," he explained. "When I was on the field with the national team, I felt my legs were shaking.
"It feels invested with greater responsibility. It is a nation – you can make the joy or the sadness of millions of people."Even today, when I hear the national anthem on the TV before games, I have the same particular emotion."