Chairman David Sullivan says captain Declan Rice has probably played his last game for West Ham after being "promised" he could leave this summer.
The 24-year-old England midfielder has been heavily linked with a move away from London Stadium.
Asked if Wednesday's Europa Conference League triumph over Fiorentina was his last Hammers appearance, Sullivan told Talksport: "I think it has to be.
"We promised him he could go. He set his heart on going."
On Wednesday, Rice became only the third West Ham captain to win a trophy for the club, following in the footsteps of the great Bobby Moore, who lifted the Cup Winners' Cup in 1965 and club legend Billy Bonds, who led the Hammers to the FA Cup in 1975 and 1980.
Rice has made 245 appearances in total for the east London club, scoring 15 goals having made his debut during the 2016-17 campaign after coming through the club's academy system.
He also represented the Republic of Ireland three times before switching his international allegiance to England, for whom he has been capped 41 times, playing in all five of their matches at the World Cup last November and December.
Rice currently has one year left on his contract at the club, with the Hammers having the option to extend that until the summer of 2025, leaving them in a strong position to negotiate a substantial transfer fee.
"You can't ask for a man who has committed more to us this season," Sullivan added.
"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 £10m 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. 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.