The Mariners, second from bottom of the Football League, sacked Newell on Monday following a fourth successive league defeat.
Chairman John Fenty has already gone on record as stating that the club could follow the lead of rivals Lincoln and appoint a novice manager - the Imps handed Chris Sutton his first post at the end of last month.
Dean Windass, who was recently Colin Todd's assistant at Darlington before the two were sacked, has expressed his interest in taking his first steps in management at Blundell Park.
However, Powell, who led England to the final of the European Championships this summer, would create history as the first female to ever manage a professional men's football team should she be appointed.
The Football Association, Powell's employers, have denied knowledge of the story, but League Managers' Association chief executive Richard Bevan told Sky Sports News: "Why shouldn't she (make the step into the men's game)? Hope has done a fantastic job with England, but I'm not sure the FA would want to let her go."