It looks like West Ham winning the Europa Conference League will be Rice's final act as a West Ham player, Hammers co-owner David Sullivan admitting as much on talkSPORT earlier on Thursday.
talkSPORT understands Arsenal are the favourites to sign Rice with Manchester United and Bayern Munich also linked.
However, prominent West Ham fan and actor Dyer cannot picture the midfielder in Arsenal colours, insisting the Gunners' shirt doesn't suit him.
Speaking to Andy Goldstein and Darren Bent on talkSPORT, Dyer was asked about Sullivan's interview.
Dyer responded: "It's a shame, mate. It is awful.
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"I can't imagine him in another shirt. I've been there since the beginning of his journey and he loves the club.
"We just won a trophy, he wants trophies, he's got one. So, where is he going?
"I can't imagine him in an Arsenal shirt, I just can't. It don't suit him. I mean think about it."
Rice was asked about his future after the game in Prague on the pitch and gave hope to the Hammers as he revealed his love for the club.
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The London-born star has a contract that expires at the end of next season but there is an option to extend by another year.
And Dyer referred to his post-match interview to indicate that he might have had a change of heart due to West Ham's success in Europe.
Though he did admit that any transfer away would have him feeling quite emotional.
The 45-year-old added: "I think it is going to be very different without Declan Rice but he done his interview last night, said he loves the club and has two years left.
"That was coming out of his mouth, then obviously Sullivan… he's a strange old cat, he was running around in a velvet jacket last night.
"He says it how it is, offered him 200 bags, he said no to it but that was then and this is now.
"I think I may shed some tears when he leaves actually."
West Ham will demand a hefty fee for his services in any situation and it could turn into a bidding war with prices deemed as high as £100million.