Allardyce, who has been in charge for almost four years, is expected to leave Upton Park in the summer when his contract expires.
That would leave West Ham needing a new manager in their final season at Upton Park before the move to the Olympic Stadium in 2016 - and the Hammers hierarchy could look to make an ambitious appointment.
The London Evening Standard believe that David Moyes and Slaven Bilic are in the running having impressed with Real Sociedad and Besiktas respectively, but they also raise the possibility of Rafa Benitez making a shock return to the Premier League with West Ham.
The Spaniard is currently managing in Italy with Napoli, but will also be out of contract come the summer - and the London Evening Standard report that West Ham are considering a move to hire Benitez.
The 54-year-old famously won the Champions League during his time in charge of Liverpool, and boasts a 51% win percentage over his career as manager of Real Madrid B, Villarreal, Osasuna, Extremadura, Tenerife, Valencia, Liverpool, Inter Milan, Chelsea and Napoli.
Benitez would be a surprise, ambitious appointment for West Ham - but they must first let Allardyce leave the club before really pursuing a new manager.