Ex-Rotherham United man made favourite to land job with Doncaster Rovers and Bradford City's League Two rivals
The Mariners are yet to unveil a replacement for Paul Hurst, who they opted to axe nearly a month ago.
Artell has been made favourite to fill the Grimsby vacancy by BetVictor, with a price of 2/5.
A defender in his playing days, Artell began his career with hometown club Rotherham.
He went on to be a well-travelled player, representing the likes of Mansfield Town, Morecambe and Wrexham, as well as the Gibraltar national team.
Artell stepped into management with Crewe Alexandra and spent five years in charge of the club, being dismissed in 2022.
He has been out of work since, although has been among the favourites with bookmakers for various posts.
At 2/5, he is the clear favourite and sits comfortably ahead of second favourite Shaun Pearson.
Outside contenders include Justin Cochrane at 16/1 and David Healy at 25/1.