Coral had the former Everton and Manchester United boss on 3/1 but he has become the new favourite after a flurry of bets placed on him this morning.
Scotland Under-21 coach Scot Gemmill is currently second on 11/8 while Kilmarnock manager Steve Clarke remains popular at 3/1.
John Hill, spokesman for Coral, said: “We have been knocked over with interest in David Moyes in the last 24 hours and, as a result, the former Everton and Manchester United manager is now the new favourite to get the job.”
Moyes, who has also had managerial stints at Real Sociedad in Spain, Sunderland and West Ham attended three Scottish Premiership matches this past weekend - Celtic’s home match with Kilmarnock, St Mirren v St Johnstone at the Simple Digital Arena and Rangers’ 2-0 win over Aberdeen at Ibrox.
Elsewhere in the betting, Moyes’ fellow ex-Hammers boss Slaven Bilic is at 9/1, ex-England manager Sven Goran Eriksson is at 10/1, Aberdeen’s Derek McInnes is at 14/1, current Scottish FA Performance Director Malky Mackay is at 16/1, Walter Smith 18/1 and Hearts boss Craig Levein a surprise candidate at 20/1.