The Daily Mirror is reporting that the Red Devils want to sign the 26-year-old defender to bolster their back line but as things stand, the player himself would prefer a move to Manchester City.
However, Manchester City will turn their attentions to other defensive targets if Leicester City refuse to budge on their £90m valuation of Maguire.
And that could hand Manchester United a significant boost as they look to try and bring the England international to Old Trafford this summer.
According to the same story, however, both Manchester clubs could face a battle in convincing Leicester to sell the defender, as the Foxes want to keep hold of Maguire this summer.
Maguire scored three goals in 31 Premier League games for Leicester City last season.
Manchester United are thought to be on the lookout for a number of new signings this summer as they look to rebuild following their sixth-placed finish in the table last term.
The Red Devils have already agreed a deal with Swansea City to land midfielder Daniel James this summer.
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