The Red Devils are desperate to snare the England international this month.
Former Old Trafford chief Jose Mourinho wanted him after the 2018 World Cup.
However, chief executive Ed Woodward refused to authorise a mega-money raid for the Leicester man.
This summer is different, though. Ole Gunnar Solskjaer is similarly keen to get a deal done and United are ready to back the club legend.
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“Leicester ace Harry Maguire is wanted by Man Utd and Man City”
Nevertheless, according to The Sun, United look set to to face a tug-of-war with City.
Both clubs have had £65m offers rebuffed by the Foxes, but City remain serious suitors.
The Sun say City believe they can still lure Maguire to the Etihad and will consider making their move at the 11th hour.
United have already snapped up Aaron Wan-Bissaka and Daniel James this summer.
But both stars are relatively inexperienced and Solskjaer is also expected to add proven quality to his ranks.
“We’re still in the market looking to do some business, as I’ve said before,” he said.
“But we’re patient, we’re Man United, we don’t have to sell and don’t have to overpay either. You have to have the right players at the right price.
“And if you look at the squad we’ve got now, there are so many good players anyway.
“I’m sure with a good pre-season behind us – that’s the main thing now – the ones who are here are working hard want to improve.
“It’s not just about fitness work, it’s about robustness, this squad needs to be more robust when the season gets going.
“Last year, we had a run of I don’t know how many games without any defeats but the end was disappointing because we couldn’t get back to winning ways and need to get back to that.
“Doing business in the football market is not going to be a quick fix overnight. And we have players here who I trust.
“There are fantastic players here, loads of players I know are gonna be successful at this club and we’ve signed two in Dan and Aaron, with their speed and hunger, with quality that will be part of that.
“And I’m coaching and managing them here, the business side of it is you have to be in the market and, as I said, we don’t have any offers for our players.”