West Ham want the Scot and he wants a return to England, says a report.
Indeed, the ex-Manchester United and Everton manager is said to want a Premier League return, with Real Sociedad not standing in his way should he want to leave the La Liga outfit.
According to sports betting website Oddschecker, Moyes is second-favourite to succeed Allardyce at West Ham - with former Liverpool boss Rafa Benitez leading the way.
But there may be a slight issue for the Hammers regarding their leading candidates.
Indeed, while the club appear dissatisfied with Big Sam (whose contract runs out at the end of the current campaign), those linked with replacing him are very much being deemed surplus to requirements at their current teams.
The Mirror's report suggests Moyes is not seen as a long-term option by Sociedad; Benitez may no longer be wanted by Napoli (hence his reported availability); Gus Poyet was sacked by Sunderland; Marcelo Bielsa isn't cutting it at Marseille.
Moyes, too, plays a similar brand of football to Allardyce. But if he's the man West Ham want, it appears the pathway is clear based on this latest report.