The defender has been linked with a move away from the Boleyn Ground for much of the season as his contract expires in the summer with the New Zealand international apparently unwilling to sign a new deal with the Hammers.
Allardyce told reporters at his pre-match press conference ahead of his side's FA Cup tie with Everton:
"There is no future for Winston Reid at West Ham at the moment because his contract ends on June 30.
"I would say it's highly unlikely that Winston is going to sign for us based on what people have said to me."
It would seem the paper talk has some weight to it with Reid edging closer to the exit door. Both Liverpool and Arsenal have been linked with a move for Reid over the course of the season. Arsenal have been short on defensive numbers for large parts of the campaign, whilst Liverpool's defensive frailties are well documented, and as a result they have been linked with bringing in reinforcements.
Manchester United have also been a side mentioned in connection with Reid given the troubles they have had with their back line this season, but it will be interesting to see what Reid's next move is.
The 26-year-old has been an important part of the West Ham side this season having missed just the one Premier League game, so this is a big blow for the Hammers as Allardyce may feel the need to bring in another defender to compensate for his loss.