Reid has emerged as a target for Everton in recent weeks, with reports suggesting they are preparing a £9million bid for the 29-year-old.
Everton manager Ronald Koeman is said to have set his sights on the New Zealand international as cover for Ramiro Funes Mori.
But according to the London Evening Standard, West Ham are prepared to reject any approach from the Toffees for their vice-captain.
West Ham playmaker Manuel Lanzini has also been linked with a move away from the London Stadium this summer.
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Slaven Bilic wants to keep Winston Reid at West Ham
The Argentina international is said to have attracted interest from Liverpool as the Reds prepare for life without Barcelona target Philippe Coutinho.
But like with Reid, West Ham are unwilling to entertain offers for the 24-year-old.
And while West Ham are keen to keep their star players, manager Slaven Bilic recently admitted he is in the market for new arrivals.
The Hammers have spent in excess of £40m on signings so far this summer, with Marko Arnautovic, Javier Hernandez, Joe Hart and Pablo Zabaleta all joining.
West Ham will not sell Everton target Winston Reid
"Make no mistake, we are working hard every day, but it is not easy," Bilic said of West Ham's transfer plans.
“Some clubs, like Everton, are signing a lot of players, some are signing a couple of players, and some haven't signed any.
"But that doesn't mean they are not trying. I'm sure everybody is working, and everybody is trying to sign players.
“What we want is to bring in the quality that is going to improve our first XI."
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