The Scot has been out of work since leaving Nottingham Forest at the end of last season and attracted a run of bets on Tuesday, prompting his price to be slashed from 25/1.
Adkins had been favourite ever since being sacking by Southampton on Friday, but has now drifted out to 2/1 amid suggestions of a lack of interest from his part.
Caretaker boss Steve Thompson is 5/1 to fill the post on a permanent basis, having led the Seasiders to three successive defeats since Michael Appleton departed on January 11.
Sky Bet Football Trader Chris Spicer said: "We were somewhat surprised how much support Adkins attracted for the post, with the former Saints manager's CV surely warranting a more lucrative post given what he achieved at St Mary's.
"Backing for Billy Davies to take the job begun on Tuesday morning and has continued ever since despite us cutting the price several times, but it seems another slightly strange one given his availability and the amount of time which has passed since Appleton's departure."