While Maguire has the backing of manager Erik ten Hag and will remain United captain next season, he was repeatedly booed by his own supporters during a recent pre-season friendly against Crystal Palace.
The centre-back had similar jeers aimed towards him at the end of last season in response to poor performances, but Varane believes his fellow 29-year-old will bounce back even stronger than before.
‘I think he’s a very important player for us,’ the French World Cup winner said in the pre-match press conference ahead of Saturday’s friendly against Aston Villa.
‘He’s the captain and he has a lot of great qualities. Obviously, we support him and he’s part of the team and very important for us.’
When fit, Maguire and Varane were United’s first-choice centre-back pairing last season, but with Ajax’s Lisandro Martinez set to join the side that partnership could be under threat.
But Varane thinks it will only improve their performances, adding: ‘I think the competition is very good for the team. We’ll all be better with this competition.
‘It’s good for the team, so every great club is like this. So, this is normal.
‘I think we have to be ready for this pressure. If everyone wants to fight for the team, that’s great news.
‘We try to play with the defence, and we try to defend very high on the pitch, so with more space on our back. I think it’s a football that is maybe more offensive. But this football we really enjoy, so that’s a good start.’
Ronaldo meanwhile did not travel on the Red Devils’ tour of Australia and Asia after demanding to leave Old Trafford after the club failed to qualify for next season’s Champions League, although United are unwilling to sell the star forward.
Varane played alongside Ronaldo at Real Madrid for seven years, so he fully understands the Portuguese’s feeling at the moment, but has urged him to stay and help re-build the team.
‘Cristiano is a great competitor, he’s a legend. Obviously, it’s very good to play with him and he always helps the team.
‘He’s a great player and we all want the best players in the team. We will try to improve next season.
‘We appreciate him as a player and as a person. We know his quality and we know he’s very famous, so we know a lot of people will speak about the performance of the team and his performance.’
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