The New Zealand centre-back is out of contract in June and is reportedly thought to be interesting West Ham’s London rivals Arsenal.
Reid is in his fifth season at Upton Park, however, Allardyce – who slapped a £20million price tag on the former Midtjylland man last month – does not anticipate the 26-year-old will be extending that stay to a sixth.
Allardyce said: “I would say it’s highly unlikely that Winston is going to sign for us based on what people have said to me.”
Doneil Henry, a Canadian centre-back, has already been signed by West Ham this month and will keep Allardyce’s options well-stocked if the Kiwi captain moves on.
West Ham take on Everton in the FA Cup third round on Tuesday and will be without Cheikhou Kouyate and Diafra Sakho, who are set to compete for Senegal at the Africa Cup of Nations.
Defender James Tomkins is also a doubt with a twisted ankle but Allardyce is hopeful they can take advantage of an Everton side on a run of four straight defeats.
“Last year Everton didn’t have the injuries they’ve had this year and it’s very difficult to overcome that, especially at the back,” Allardyce added.
“If there’s a lack of confidence there on Tuesday then hopefully we’ll take advantage of that.”
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