The Independent, as quoted by Metro, is reporting that Manchester United are keen to bring the 20-year-old to Old Trafford as they look to bolster their squad this summer.
The same story claims that both clubs have opened talks about a possible deal, but the player himself could now stand in the way of a potential transfer.
According to the same article, Rice is not keen to join Manchester United in their current state – and he is set to join the likes of Jadon Sancho in snubbing a move to Old Trafford.
Rice was in impressive form for West Ham United last season, and he scored two goals in 34 Premier League appearances for the Hammers.
Manchester United are thought to be on the lookout for a number of new signings this summer as Ole Gunnar Solskjaer looks to strengthen his squad ahead of his first full season in charge.
The Red Devils finished in sixth place in the Premier League table and without a trophy last term under Solskjaer.
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