Sullivan told talkSPORT that Rice has played his last game for the Hammers following their Europa Conference League victory.
The 24-year-old lifted the trophy in Prague after a 2-1 win over Fiorentina, in a glorious farewell.
Rice turned down a lucrative contract offer 18 months ago, meaning it has cost him millions by staying at the club.
He has one-year left on his current deal and West Ham will now listen to offers this summer.
When asked if it was his last game, Sullivan told talkSPORT: "I think it has to be.
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"We promised him he could go. He set his heart on going.
"You can't ask for a man who has committed more to us this season.
"In due course, he has to get on and we have to get a replacement - or several replacements.
"It's not something we want to happen. We offered him £200,000-a-week 18 months ago. He turned it down.
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"It's cost him £10million to stay at West Ham in that time (in lost wages). And he wants to go.
"You can't keep a player who doesn't want to be there."
talkSPORT understands Arsenal will now ramp up their interest in Rice following the Europa Conference League final.
The Gunners target was asked about his future immediately after that win and was coy about what might happen this summer.
Rice told BT Sport: "Look, at the moment there's obviously a lot of speculation going on about my future.
"Obviously there is interest from other clubs, that's out there, but ultimately I've still got two years left at West Ham.
"I love this club, I love playing for this club, there hasn't been nothing yet.
"So my focus is playing for West Ham, enjoying tonight and seeing what happens.
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"I'm captain of this club and I absolutely love it to pieces, I cannot speak highly enough of this place and let's just see what happens."
Pressed whether this is the best way to potentially bow out in a West Ham shirt, the England international stated: "Let's wait and see, who knows?"