Rashford has enjoyed his most productive season in terms of goals in 2019-20, scoring 19 in all competitions for the Red Devils despite being sidelined since January due to a back injury.
The England international burst onto the scene early in 2016 under Louis van Gaal, finding the net twice on both his Europa League and Premier League debuts after coming through the club's academy system.
Darmian, however, is not surprised at the 22-year-old's continued development since then, having seen at close quarters just how good the forward is.
"I still remember Marcus Rashford's first session with the senior squad like it was yesterday. I immediately thought, 'wow, this is an incredible player'," he told the Guardian.
"He did so many impressive things for a player of his age and the way he improved in every detail really impressed me."
The Italian defender, who returned to his homeland last September by signing for Parma, feels the England international can still get even better, too.
Darmian feels Rashford has the potential to match Paris Saint-Germain superstar Mbappe, the pair perhaps competing for individual honors for many years to come.
"If he [Rashford] continues to work the way he has done so far he can be a Ballon d'Or winner. I'm convinced of this," he said.
"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."
"I can only speak well about Solskjaer, believe me," Darmian said of the Norwegian. "I would give him a long-term contract.
"He's a very prepared coach and Manchester United has started this project, this journey, with many young players, many British players and they will continue with this project.
"Because of the person I got to know, I hope Solskjaer has success at the club."