The Gunners are in a battle with Premier League champions Man City to sign Rice but remain quietly confident of winning the race.
Arsenal identified Rice as their top summer target several months ago and have tabled two offers for the England star, the second worth £90m.
But West Ham value Rice, 24, at £100m and were not only unhappy with the money on the table but also how Arsenal’s deal was structured.
Manchester City tempted West Ham with their first bid on Monday night but again, the offer worth £90m in total was knocked back.
Since Man City’s opening bid, Arsenal have informed West Ham of their intention to return with a third offer for Rice which, according to the Daily Mail, was seen by both parties as effectively a verbal offer.
It is claimed Arsenal’s next bid will be within touching distance of West Ham’s valuation for a player who has made 245 appearances for the Hammers, many as captain.
Rice has not only emerged as West Ham’s most important player in recent seasons but also a key member of Gareth Southgate’s England squad, featuring heavily at last year’s Qatar World Cup.
If Rice does leave east London this summer, he will have helped West Ham win the Europa Conference League – their first major trophy since 1980 – in his final game for the club.
Manchester United have also been tentatively linked with the Hammers hero but John Barnes believes Rice should secure a move to the Emirates Stadium.
‘Arsenal have made two bids for which will probably get up to £100m so Arsenal makes more sense,’ the ex-England star told futfanatico.com.
‘Not because they’re better than Man City but because Arsenal are more interested and I think he wants to go to Arsenal. That will be the best thing for him.
‘Rice will fit into Arsenal’s way of playing in that holding midfield role. £100m for Rice means he goes straight into that Arsenal team as the holding midfielder.
‘Protecting that back four and bringing solidity, which is what the Arsenal team needs.
‘I don’t think Manchester City are as interested in Declan Rice because they’ve got Rodri. And I don’t think Pep wants two holding midfielders.’
Rice looks set to either join a Man City side that won the treble last season or an Arsenal team that sat top of the Premier League for 248 days.
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