Italian Gimondi won the Tour in 1965, Giro in 1967, 1969 and 1976, and the Vuelta in 1968, joining an elite club of riders who have achieved the 'triple crown'.
The 75-year-old says that Froome is perfectly placed to join this club when he attempts the Giro in 2018 and establish himself as "one of the greatest riders ever".
"Froome can do it," said Gimondi.
"It's difficult to outdistance him on the climbs, because he's properly skilled and supported by a strong team.
"He can also perform well in the TT stages, without losing too much from specialists like Dumoulin.
"Anyway, the battle will include other riders, starting from Aru, who won't give up before having played all his cards".
Froome is aiming to do something that Gimondi did not achieve in his career: winning more than one Grand Tour in the same year.
Gimondi attempted the Giro-Tour double in 1967, but his plans came unstuck when he fell ill in France.
"I thought I could get it at the Tour: I was in a brilliant shape, but some intestinal problems knocked me out," said Gimondi of his 1967 Tour.
"We were on riding on the Pyrenees, I was looking for water since 30 kilometers: I took a bottle of cold water from the service van of the Tour and I drank it in one shot."
Aside from Gimondi, only five other riders have claimed victory in all three Grand Tours: Jacques Anquetil, Eddy Merckx, Bernard Hinault, Alberto Contador and Vincenzo Nibali. No rider has ever won all three races in the same year.
Merckx tops the table of Grand Tour winners, having claimed 11 in his unrivalled career.
Gimondi has remained actively involved in the cycling world since retiring, and designed the routes for the Gran Fondo Gimondi Bianchi on May 8 in Bergamo, Italy.
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