West Ham are said to be considering the 57-year-old.
West Ham lost 2-1 in the Premier League to bottom club Leicester City on Saturday afternoon and speculation has surrounded their manager's future for some time.
And the reason the club's owners are drawn to Hoddle is reportedly the style of football his sides play - something supporters have not seen from Allardyce over the years.
Elsewhere, the Daily Mail suggest Marcelo Bielsa is the frontrunner for the West Ham job, although that isn't a particularly new rumour.
With regards to Allardyce, although nothing has been confirmed about the coach's future, a parting of the ways looks increasingly as though it could be the right way to go.
The 60-year-old has done a fine job at Upton Park in many ways but, at the same time, appears as though he can only take clubs so far.
West Ham's owners appear to want something new, different. Whether Hoddle is quite the answer remains to be seen.
Caution must be exercised, as the one thing the Hammers have built up under Big Sam is stability. But it certainly seems the east London side need someone fresh.