The England international is valued at more than £100m by the Hammers and they’re resigned to losing the midfielder this summer.
Arsenal’s last bid was worth around £90m, but £15m of that was in add-ons.
West Ham were also unhappy with the make-up of the bid, with the £75m fee coming in five installments over the next five years.
City have bided their time in the running but the Athletic say they will now submit a bid for RIce today.
With Ilkay Gundogan set to join Barcelona, Pep Guardiola wants to strengthen his midfield.
City possess greater financial muscle than Arsenal but it remains to be seen whether Rice would rather remain in London.
West Ham want more than £100m for the midfielder and can be confident of getting their asking price now that City have entered the running.
Manchester United hold an interest in Rice but cannot afford a £100m+ fee alongside their other planned business.
Scott McTominay and Harry Maguire are both targets for West Ham, and could be offered in part-exchange.
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