The Gunners are in a battle with Manchester City to land Rice, and The Athletic are now reporting their latest bid is structured as £100 million with £5m in add-ons.
Should West Ham accept the offer, it would set a new transfer record for a British player.
Arsenal previously put forward a £90m package for the England international standing at £75m plus £15m in add-ons which was turned down by the Hammers.
City, meanwhile, made a formal offer of £80m with £10m in add-ons but were also met with a swift rejection.
Rice has one more year remaining on his current West Ham deal, but all signs point towards an exit this summer after chairman David Sullivan said he is expecting a departure.
He has made 245 appearances for the East London club and captained the side to European glory in the Europa Conference League.