The 2016 champions had been holding out for a deal worth £80m in total, and United are understood to have come up with acceptable terms, with around £10m wrapped up in conditional clauses.
Maguire last week told Leicester he wanted to leave, and the club agreed they would not stand in his way, so long as their requirements were met.
United staff members feel that the 26-year-old English international will complement the developing Victor Lindelof at the heart of a new-look defence, that will form the foundation of a fast and hard-pressing team.
The club are also working on a deal for Sporting’s Bruno Fernandes, and figuring an offer that will be acceptable to the Portuguese club.
Earlier in the week, Brendan Rodgers revealed United had previously failed to meet Leicester's price. "Harry's a top quality player and no-one has come near the valuation to tempt the club to sell," he said.
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