The Scot left West Ham earlier this week after just six months in charge, despite steering them clear of the relegation zone.
Moyes has never really settled in a role since departing Everton for Manchester United in 2013, having endured unsuccessful spells with Real Sociedad and Sunderland before joining the Hammers.
However, he could be handed a quick route back into management with reports suggesting that he is a target for Stoke.
Paul Lambert is currently in charge but it's understood there is a 'break-clause' in his contract, which would allow Stoke to send him packing.
Stoke's board have made it clear that they are looking to make big changes after suffering relegation in the hope that they can secure an immediate return to the top flight.