Sky Sports News claims that the two city rivals made enquiries about the availability of the England international.
However, the Hammers rejected their advances and have no intention of letting the 20-year-old leave.
Rice enjoyed a breakthrough season for the Premier League club in 2018/19, making 38 appearances and earning his England debut after deciding to swap allegiances from the Republic of Ireland.
The midfielder signed a new contract last December tying him down until 2024 with the option of a further year.
According to the report, City are only considering a swoop for Rice if they fail in their efforts to bring in Atletico Madrid’s Rodri, while United are prioritising other positions for now as Ole Gunnar Solskjaer builds a new-look squad for next season.
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