As a result, the road is seemingly clear for Arsenal to thrash out a deal with West Ham for their number one transfer target.
talkSPORT also understands that Rice's camp are pushing for the Hammers to accept the Arsenal bid.
Pep Guardiola's side had been heavily linked with a move for the 24-year-old and even made an offer of their own, however, this was turned down by the Hammers.
But Arsenal have since stepped up their efforts and launched a bid worth a British record £105million to finally wrap up a deal for the midfielder.
While that offer is closer to West Ham's valuation, it's understood that the east London side are looking for a faster payment structure.
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That bid meant the Gunners were confident of seeing off City's interest in the player, something that now looks to be the case.
Arsenal have always been tipped as Rice's preferred destination due to his desire to stay in London, with a move now appearing more and more likely.
Should the offer be accepted, Rice's move to Arsenal would surpass the previous record set by Manchester City when they signed Jack Grealish from Aston Villa for a fee worth £100million in 2021.
West Ham owner David Sullivan told talkSPORT last month that Rice's Europa Conference League final-winning performance would be his last game for the club.
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He has played 245 games for West Ham, having come through the club's youth system after being released by Chelsea.