Following days of speculation, Manchester City finally tabled their opening offer for the England midfielder on Monday evening.
The Premier League champions’ bid consisted of a fixed £80m fee and another £10m in add-ons for the Hammers.
The overall proposal matched Arsenal’s second bid for Rice but Manchester City are willing to offer more money in terms of a fixed fee.
However, the offer has been rejected by West Ham, who still want more money from Rice’s sale.
The east London club are prepared to sell the midfielder but are holding out for the maximum fee.
West Ham want the fee to exceed the £100m mark and are waiting for either Arsenal or Manchester City to put in a suitable offer.
The Gunners have been working on trying to sign Rice for several months and are expected to table their third bid soon.
It remains to be seen whether Manchester City come back with a second offer to keep the bidding war going.
Manchester United are also exploring the possibility of getting Rice for a player-plus cash deal but are yet to table a formal offer.