Lambert, who left Wolverhampton Wanderers at the end of last season, is evens favourite to take charge of Sheffield Wednesday.
Lambert left Wolves at the end of last season and remains a free agent.
The Scot was low down Sky Bet's list of potential Owls appointments earlier on Sunday, but a surge of bets have seen him shoot to the top - ahead of Steve McClaren (9/4) and Andre Villas-Boas (11/2).
Claudio Ranieri emerged as second favourite this morning, but has since drifted from 4/1 to 10/1, alongside Gus Poyet.
Sheffield Wednesday are currently 16th in the Championship, having finished in the play-offs in each of the previous two campaigns under Carvalhal.
Owls caretaker Lee Bullen said last week that he expects to be in charge until after Monday's league visit of Burton Albion, but could remain at the helm for Saturday's FA Cup trip to Carlisle United.
Lambert, 48, has previously managed Livingston, Wycombe Wanderers, Colchester United, Norwich City, Aston Villa, Blackburn Rovers and Wolves.
Would Lambert be a good appointment for Sheffield Wednesday?