The England international was keen on joining Chelsea last summer and Frank Lampard pushed his board to complete an £80m move for the midfielder, which would have seen Rice return to his boyhood club.
However, the Chelsea hierarchy saw little value in the move and Rice’s hopes of moving to Stamford Bridge ended with Lampard’s sacking.
The disappointment of that move collapsing has had little effect on Rice’s form this term though, with the midfielder producing the form of his career so far with the Hammers.
David Moyes’ men currently occupy the last Champions League spot but their hopes of keeping Rice may hinge on keeping that position until the season’s end as the Manchester Evening News claim he’s keen on moving to Old Trafford.
Rice reportedly spoke to Maguire and Shaw at England’s training camp earlier this month about the club and what it’s like to play under Ole Gunnar Solskjaer.
United have been in the market for a deep-lying central midfielder for the last two years, with the club anticipating the departure of Paul Pogba this summer and Nemanja Matic becoming an increasingly maligned figure.
Rice is capable of playing at centre-back but United believe he has grown into his role in central midfield, while they seem him developing into a more traditional box-to-box player in a team that enjoys a greater share of possession.
However, Moyes revealed last month that West Ham value Rice at ‘far more’ than £100m and United will likely need to break their club transfer record to sign the midfielder this summer.
The Hammers’ interest in Jesse Lingard could help to reduce the overall fee for Rice but West Ham have intimated they will not entertain any part-exchange offers to sign Lingard.