The Colombian claimed his first grand-tour victory when he won the Giro d'Italia in June.
Now Unzue says success at the 2015 Tour is the next step for Quintana, and the team manager thinks the route - which includes seven mountain stages - favours his number one rider.
"This year [2014] the best thing was to send Nairo to the Giro d’Italia because of the pressure but next year's it's fine to go to the Tour de France because he's already got a big tour under his belt," he told Cycling News.
"He's got more confidence and more experience, so he's ready.
"[Alberto] Contador, [Chris] Froome, [Vincenzo] Nibali, and Nairo - the four of them are very similar and they're the four magnificent riders in the peloton.
"It's a Tour for the four of them and they're all great climbers. They're the leading grand tour riders of their generation.
"For me Nairo is the better climber out of that bunch but at the same time he's still young and he still has a lot to discover about the Tour de France and he needs to gain experience there.
"If they stay safe in the first week then we'll see the climbers fighting it out for the victory."