Grimsby are without a win in six games and have slipped to 22nd place in League Two; despite being the only League Two team to have beaten The Saddlers this season.
Graham took charge of The Mariners five months ago when expectations were high for the up-coming campaign. Grimsby were beaten by Cheltenham Town in last season's Play-Off Final.
Watkiss has so far refused to either declare his interest or withdraw his name from the full time position at Blundell Park.