It is understood that Villa approached Norwich on Wednesday for permission to speak to Lambert but a section of the Norwich board are thought to have blocked the move, prompting the Scot's decision to quit.
Norwich have made no comment on the position of Lambert, who has steered them to two promotions and a mid-table finish in the Barclays Premier League, but Villa are hopeful they can finalise a compensation package with the Canaries for the 42-year-old who is on a rolling contract and fill the vacancy created by the sacking of Alex McLeish.
Lambert would be a popular choice amongst supporters, with polls in local newspapers favouring the former Livingston, Wycombe and Colchester manager.
That is in stark contrast to the anger at the appointment of former Birmingham boss McLeish last summer.
Villa owner Randy Lerner is hoping it will be a case of third time lucky in terms of finding a successor.
He held talks with former Manchester United star Ole Gunnar Solskjaer but he opted to stay at Molde in Norway for family reasons although he was not formally offered the Villa post.
Villa also spoke with advisers of Wigan boss Roberto Martinez who rejected the chance to replace Gerard Houllier 12 months ago. But Latics boss Dave Whelan claimed Martinez, who held talks with Liverpool, is staying put.