But things have gone poorly in recent weeks, with 10-man United's shock 2-1 loss at Young Boys in their Champions League opener compounded by the Carabao Cup exit to West Ham and Premier League loss to Aston Villa.
Ole Gunnar Solskjaer's side will look to bounce back from that run of three losses in four matches in Wednesday's Group F match against Villarreal, with Varane confident that this will prove to be just a blip.
"What I've been able to see is, with my team-mates, there's a lot of quality in our squad, in our team," the France international said. "We've got huge potential, I'm convinced of it.
"We're working really hard, we're working well in training. I think we're improving all the time. Since the start of the season I think we're on a positive, upward curve.
"I think that there's talent, there's experience there as well. We've got everything you need to have that belief that you can do well.
"I think that's a really key issue – we've got to believe in ourselves, be convinced that we can do it, we have got to be ambitious, believe in our own potential and then I think you can achieve things when you do that.
"There's everything there in the right place. Just concentrate on the little details but keep believing and have that positive mentality.
"I believe that each time we go into a game, we go on that track and keep on that road of positivity, think on how we can improve in little details and then I think we'll be there. As I say, we're on the right road."
Varane's arrival may not have led to an immediate improvement in United's backline but his quality and leadership is clear.
A World Cup winner with France in 2018, he lifted the Champions League on four occasions at Real Madrid – a club that has similar history and expectations to United.
"It's always hard to make comparisons like this," Varane said. "Big clubs are always wanting a lot of their players, they expect a lot from the players. There are a lot of demands on any player.
"I believe that it's fairly similar, I'd say. The hopes and demands and expectations at big clubs are always fairly similar.
"After a defeat or a draw, you know what it's like, it's always very negative when that happens. The key is to keep up good runs of results and be positive.
"That pressure you kind of live with it at big clubs but it's hard to say whether it's bigger in one or lesser in another. There is always a lot of expectation, for sure."