The defender, 32, is off contract in June and has fielded contact from the Saudi Pro League.
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However, United are now in negotiations with Maguire's representatives about a new agreement, says the Daily Mail.
Maguire has played his way into manager Ruben Amorim's plans over the past year and was added to the team's leadership group for this season.
The veteran will have to accept a major pay-cut to re-sign with United.