The Rossoneri legend has been impressed by the impact the former striker has made at Fiorentina and believes he could repeat the feat at San Siro
The 35-year-old, who won Serie A and the Champions League twice with AC Milan, claims the former striker has demonstrated great potential in his embryonic coaching career and tipped him to make the move to San Siro.
"He represents a fresh face and a new mentality, and his sides play good football," Gattuso told Sky Sports 24.
Montella made his name spearheading Roma's attack for a decade, with the capital club appointing him caretaker coach for a short spell in 2011.
The 38-year-old, known for his aeroplane goal celebration, took the reigns at Catania for the 2011-2012 season before being handed the Fiorentina job last summer.
The former Fulham and Sampdoria striker has steered his new club to an impressive fourth place in Serie A after 19 matches, three places better off than AC Milan.