The Canaries were looking for a new boss to replace Bryan Gunn, who they sacked last week in the wake of a 7-1 opening day loss at home to Colchester United.
Tabloid speculation had said Adkins was high on their shortlist, but Scunthorpe United said they had received no approach from the club.
Ironically they instead turned to Lambert, who leaves his position as Colchester manager to take the role.