The Hammers captain will leave the club this summer after lifting the Europa Conference League trophy in his final appearance on Wednesday.
talkSPORT understands Arsenal are leading Manchester United and Bayern Munich in the race for his signature.
When asked whether the historic victory over Fiorentina was Rice's last match in a West Ham shirt, Sullivan told talkSPORT: "I think it has to be.
"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.
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"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.
"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."
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Arsenal are expected to make an offer for Rice on Thursday after West Ham's season officially ended.
talkSPORT understands the Hammers value Rice at £120million.
The England star has 12 months left on his current contract plus the option of another year.
Sullivan officially opened the bidding on Thursday after accepting Rice's future lies elsewhere.
When asked if the Hammers have received an offer, Sullivan said: "No. But I think the offers will start to come today.
"There are three or four clubs who have shown interest, but out of respect to West Ham, while we're still playing, you don't make offers for players.
"That's not the way decent clubs do things."
Rice made more than 200 Premier League appearances for West Ham after joining the club from Chelsea's academy in 2014.
He joined Bobby Moore and Billy Bonds in Hammers folklore as the third captain to lift a major trophy in the club's 128-year history.
Speaking after the 2-1 victory in Prague on Wednesday, Rice refused to confirm a summer departure.
He said: "It's not a goodbye yet. Look at the moment there's a lot of speculation about my future.
"There is interest from other clubs, that's out there, but ultimately I've still got two years left at West Ham (one year plus option).
"There hasn't been nothing yet (offers). Let's wait and see, who knows.
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"I love every minute of it here, you can see the smile on my face. It's not about that tonight, it's about celebrating and that's what I'm going to do now."