Darmian spent four years alongside Rashford at Old Trafford before moving to Serie A side Parma at the start of the season.
The Italy international, who won the Europa League, FA Cup and League Cup at United, said Rashford can go right to the very top.
"I still remember Marcus Rashford's first session with the senior squad like it was yesterday," he told The Guardian. "I immediately thought: 'Wow, this is an incredible player.'
"He did so many impressive things for a player of his age and the way he improved in every detail really impressed me. If he continues to work the way he has done so far he can be a Ballon d'Or winner.
"I'm convinced of this. He impressed me the most of all the players at United and he's very young and can still improve. For me he can reach the level of Kylian Mbappe and compete for the Ballon d'Or for years to come."
Mbappe, ranked ESPN's No.1 player aged 21 or under, finished sixth in the 2019 Ballon d'Or final voting while Rashford was not on the list of nominees.
Darmian also said that United midfielder Paul Pogba receives a lot of criticism despite being a positive influence in the dressing room.
"There has been a lot of unjustified criticism towards Pogba, for example that he doesn't work hard enough, but he always gave his best, I can assure you, in every training session," he added.
"In my opinion his performances were good in recent years, they talk about him too negatively [in the UK].
"Did I see Pogba unhappy or willing to leave? No, I honestly didn't see him sad or unhappy, quite the opposite, for all the time I was in Manchester, Paul was absolutely happy with his decision to go back there. He really cares about doing well at Manchester United."
Pogba said he has been "frustrated" this season due to his injury problems this season but is ready to return stronger.
Sources have told ESPN United are optimistic he will remain at the club beyond the next transfer window before the sport was halted by the coronavirus pandemic.