The campaign finished in glorious fashion for the Hammers after they won the Europa Conference League with a 2-1 victory over Fiorentina in Prague.
As a result, Rice became the first Irons' skipper since Bobby Moore to lift a European trophy, with the England legend last doing so in 1965.
For the 24-year-old, it will be his final appearance for the club.
Hammers owner David Sullivan confirmed to talkSPORT that Rice has played his last game for the club.
talkSPORT understands that Arsenal are confident of securing a deal to sign Rice ahead of Manchester United and Bayern Munich who are also keen, with chief football correspondent Alex Crook saying that the Gunners are now likely to step up their pursuit.
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He said: "Declan Rice was obviously quite emotional last night as he was looking at the West Ham fans after sealing that incredible first trophy since 1980.
"I think he knows and West Ham know that in all likelihood it will be his last game.
"I think the clubs who are chasing his signature have held off from a formal approach until after that final last night.
"I expect Arsenal now to come in with a bid. I guess it comes down to the asking price.
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"Our own Jim White revealed a few weeks ago that they are looking for £100million up front, maybe rising to £120m.
"That is more than Arsenal would normally spend on a player, but Mikel Arteta is very keen on Declan Rice.
"Despite interest from Germany, Declan Rice is very keen on a move to Arsenal.
"I would expect that to ramp up now."