The Sun says Mackay will be a contender to succeed the Scot.
He took Cardiff to the Carling Cup final, where they lost to Liverpool on penalties, as well as the Championship play-offs last season.
Chris Hughton is also in the frame.
West Brom are not keen to cough up around £2.5million for the Birmingham man's services.
But that figure would not worry Norwich who expect to receive some compensation from Villa when Lambert is officially installed as boss.