The 32-year-old has been linked with a move away from the London Stadium before the 11pm deadline on Tuesday night.
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As well as Forest, West Ham's relegation rivals Everton and Wolves have also been touted as possible destinations for the Jamaica international.
Antonio has been plagued by inconsistent performances this season - chipping in with just two goals and as many assists from 19 top-flight outings.
But West Ham aren't willing to allow their all-time Premier League top scorer to depart with strikers Gianluca Scamacca and Danny Ings currently sidelined with knee injuries.
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And there is every chance that Antonio starts for the Hammers away at Derby in their FA Cup fourth round clash on Monday night.
Providing an update on Antonio's future, talkSPORT host Jim White has declared the centre-forward will not be returning to the City Ground - the club he left for West Ham in 2015.
Speaking on the White and Jordan show, he said: "Questions are being asked this lunchtime about Michail Antonio, has he played his final game for West Ham? I would suggest not.
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"The news coming out of West Ham to me this lunchtime is, that in spite of a hard and fast bid on the table from Forest, Michail Antonio will be staying at the football club after 11pm tomorrow night."
Former West Ham and Forest defender Stuart Pearce then stated that Antonio could help the Reds avoid relegation, but told the east London outfit to keep hold of the player.
He remarked: "I don't see what pluses there are for West Ham at the moment to move one of their strikers on. I don't think Mich's been on very good form I've got to say.
"But if someone's coming with a £10million-plus offer for him, then you think, 'well it might be worth taking the chance.'
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"Otherwise, what are you going to do? You're going to be giving one of your strikers that the fans like at West Ham to one of your rivals potentially at the bottom of the table as it stands at the moment.
"Mich could comfortably go to Forest and get seven or eight goals between now and the end of the season and that would keep Forest in the division.
"Why would you do that, for I think we're talking £2m, why would you do it? What's the point?"
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Interjecting, White stated: "It doesn't make sense, I can understand it from West Ham's point of view, Scamacca, we don't know when he is coming back.
"We don't know when Ings is going to be back. So all of a sudden, Michail Antonio, 'we need you to get in.'"
Pearce then said: "If he was on the bench and not getting on, you could say, 'well it might be worth getting him off the wage bill,' that type of thing.
"The fact he's starting - he started the last game - chances are he might be starting tonight."
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