Southgate’s England contract expires at the end of the year and he is yet to agree a new deal to keep him in charge until the 2026 World Cup.
With the European Championship in Germany later this year potentially marking the end of Southgate’s reign, United have been mooted as a possible destination for the England boss.
A move to Old Trafford would put Southgate back in charge of United defender Maguire after he retained faith in the centre-back during his past issues on and off the pitch.
But while Maguire might benefit from Southgate replacing Erik ten Hag at United, the 31-year-old insisted he wants his international boss to remain in charge for the long-term.
“Yes, definitely,” Maguire said on Thursday when asked if he wanted to see Southgate prolong his England stint.
“I don’t know what’s going to happen after the Euros, I don’t know if he knows what’s going to happen.
“But I feel like what he’s done from when he first took over this job to where we are at now, we’ve taken huge strides and he’s a massive part of that.”
Southgate is preparing to lead England into the fourth tournament of his reign.
He has come painfully close to winning England’s first men’s major trophy since the 1966 World Cup.
England reached the 2018 World Cup semi-finals, lost the Euro 2020 final to Italy on penalties and were beaten by France in the World Cup quarter-finals in 2022.
Asked if anything other than winning the Euros would be deemed as a failure this time, Maguire said: “I feel as a group we’re ready to win.
“If you asked every single player in the squad they’d say the expectation is to win the tournament.
“However, we do understand that it’s tournament football and if we are going to win the Euros, you are probably going to have to win a penalty shoot-out, so you are going to have to be prepared on that aspect.”
During Southgate’s spell in charge, he has supported Maguire even when he was out of the United team, had been stripped of the captaincy and was being jeered by England fans.
Speaking ahead of England’s friendlies against Brazil on Saturday and Belgium on Tuesday, Maguire said: “I think that the faith and the trust that he has shown me throughout my time for England has been brilliant.
“So it gives me great confidence and belief that I can turn things around. It gave me the belief in myself and he has been a huge part of that and I can only thank him for the support.”
