The New Zealand international, who has been linked with Liverpool, Tottenham and Arsenal, is currently under contract with the Hammers until the end of the season and is yet to sign a new deal at Upton Park.
Allardyce insisted he would rather allow the 26-year-old to leave on a free transfer than sell him for big-money in January.
“He isn’t going anywhere,” Sky Sports News quotes Allardyce as saying. “He is not going anywhere unless someone bids £20m or something like that. There is obviously not a lot I can do about that.”
Reid has established himself a key part of West Ham’s regular first team and helping the club climbing to fourth in the league table, sitting ahead of Arsenal and Liverpool.