Rice led West Ham to the Europa Conference League title earlier in JuneArsenal have submitted a third bid worth £105m for West Ham and England midfielder Declan Rice.
The Gunners have had two bids for the 24-year-old rejected after their offers fell short of the £100m West Ham want.
However, it is understood the Hammers do not believe the structure of the latest bid is right.
On Tuesday, West Ham also rejected a £90m bid from Treble winners Manchester City for Rice, whose contract expires in 2024.
His current deal at the London Stadium has the option for a one-year extension until the summer of 2025.
If Arsenal's bid of an initial £100m plus £5m in add-ons is successful, the initial fee would equal the British record Manchester City paid for midfielder Jack Grealish.
Earlier this month, England midfielder Jude Bellingham signed for Real Madrid for an initial £88.5m, although that deal could reach £115m if add-ons are activated.
Following the club's Europa Conference League victory over Fiorentina earlier this month, chairman David Sullivan said he was "99%" sure Rice would leave West Ham this summer.
Rice has scored 15 goals in 245 games for West Ham, having made his debut in the 2016-17 season after coming through the academy.
He has been capped 41 times by England, playing in all five of their matches at last winter's World Cup.
