Allardyce, 60, is out of contract at the end of the season, and looks set to leave West Ham after a disappointing second half of the campaign.
West Ham have won just twice in 2015, dropping off after a superb first half of the season - and the recent form has piled pressure on Allardyce again.
Fans are keen for Allardyce to leave at the end of his contract, and the London Evening Standard recently reported that the West Ham hierarchy had lined up Slaven Bilic, David Moyes or Rafael Benitez to be the club's new manager if - or when - Allardyce leaves.
It seems that 'Big Sam' may not have long to wait before getting back into work should he leave Upton Park though, with the Daily Mirror reporting that Queens Park Rangers could make a move to appoint him at the end of the season.
The R's saw Harry Redknapp leave Loftus Road in February, and they have won just once since the appointment of Chris Ramsey until the end of the season.
QPR look likely to be relegated back to the Championship on current form, and it would be interesting to see whether Allardyce would be willing to drop down to the second tier - which he did almost four years ago in order to join West Ham.
Staying in London may be appealing to Allardyce though, as it grows increasingly likely that he will be leaving Upton Park this summer.