City are weighing up an official move for the Hammers skipper with the London club now anticipating that one is imminent.
Arsenal have already seen two bids for Rice turned down, the latest a bid worth £90million.
Rice’s preference has been to join the Emirates Stadium club.
But it now remains to be seen whether City’s emergence as a genuine contender for his signature sparks a change in heart.
Arsenal will return with a third offer for No 1 target Rice.
As revealed by Mail Sport on Tuesday – the Gunners’ new bid, believed to be worth £75m in guaranteed cash with an extra £15m in add ons – was turned down as the Hammers continue to hold out for a minimum £100m.
Well-placed sources had indicated an expectation that Arsenal’s second offer would be worth a minimum £90m plus further performance-related incentives pushing the deal closer to £100m.
However, it fell short of Hammers chairman David Sullivan’s valuation. An original bid worth £80m was turned down earlier this month.
It has been indicated to Mail Sport that Arsenal are willing to meet Rice’s £100m valuation. Their next offer will be closer to that mark.
Personal terms – well in-excess of £200,000-a-week – will be formally sealed quickly once West Ham and Arsenal agree a fee.
But it remains to be seen if City’s interest scuppers the expectation that Rice will move to Arsenal.