The likes of Los Angeles Galaxy, Monaco and Juventus have all been linked with Lampard in recent weeks, whilst clubs from across Asia are also said to be keen on securing his signature after it became apparent that his services were no longer required at Stamford Bridge.
But, after Fiorentina's sporting director Daniele Prade ruled out a deal due to the player's required wages, Montella has revealed his wish for Lampard to join the Viola.
"Lampard to Fiorentina?" Montella said.
"I'd like to coach him. It's a pride that he appreciates Florence and Fiorentina.
"It would be nice, but he would also accept being on the bench.
"When I was in London I saw how he trained. He is a great professional and is physically intact."
Fiorentina are enjoying a successful season, and sit fourth in Serie A.