The Villains chief is known to be a huge fan of the Republic of Ireland star, and has been alerted by his current first-team issues at Carrow Road.
Despite having started the Canaries’ last two games, the 31-year-old is no longer seen as a key player by Chris Hughton, and has often been confined to the bench this season.
This has alerted Lambert, who is keen to add some inventiveness and guild to his side over the coming weeks.
He is confident that a £1.5m offer may be enough to convince his former side to sell, and that Hoolahan himself will be eager to push for a transfer in a bid to secure regular playing time.
Although the Villa chief is thought to be targeting younger players to build a squad for the future, he is said to be attracted to the playmaker despite his age being north of the 30 mark.