Man Utd are allegedly leading rivals City in the race to sign Maguire.
Virgil van Dijk's £75m move to Liverpool is the current record.
Maguire moved to Leicester from Hull City in a £17m deal in the 2017 summer transfer window after he impressed for the Tigers in their last season in the top flight.
United will reportedly have to part ways with more than the £75m Liverpool paid for Virgil van Dijk in January previous year if they are to sign Maguire.
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Amidst this, the 26-year-old defender fueled the speculations of his transfers, after a report according to Skysports suggest that the English International wants to join Manchester United and desires to emulate Rio Ferdinand at his probable new destination.
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"I've been in this position a number of times and it's never easy but he's taken part in everything and hasn't showed anything other than sheer professionalism".
Manchester United are closing in on one of their chief targets, Harry Maguire, who is reportedly set to join the Red Devils.
The interest did not stop Rodgers giving Maguire a 45-minute run-out at Glanford Park, helping his side keep a clean sheet.
Manchester United then spent £50m on Crystal Palace full-back Aaron Wan-Bissaka to reinforce their defence after conceding 54 times in the Premier League last term.