According to Gianluca Di Marzio, the treble-winners are confident of signing the West Ham star with the club close to a final agreement to sign him.
The Hammers value Rice at more than £100million, a figure that any club will need to match if they're to complete a deal for the 24-year-old.
Should Man City strike a deal for the England international, it'd be a significant blow for Arsenal.
The Gunners have already made two offers for Rice this summer with the latest coming last week in the shape of an offer worth up to £90million.
Despite being a club-record offer, Arsenal's bid was rejected by West Ham due to it being below their valuation.
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Now it seems that Mikel Arteta's side are at risk of missing out on their top summer target.
Rice has just 12 months left on his contract at the London Stadium, however West Ham do have the option to extend that by a further 12 months, meaning that they're under no pressure to sell on the cheap.
The midfielder was said to favour a move to Arsenal, however that could now change given the opportunity to join Pep Guardiola's treble-winning side.