The 34-year-old is the 5/6 odds-on favourite for the vacant position on SkyBet.
Grimsby are in the hunt for a new manager to replace Michael Jolley, who was sacked after a poor run of results.
Other names in the frame for the Mariners are former Premier League midfielder Kevin Nolan, their ex-player Chris Hargreaves, Robbie Stockdale and current caretaker manager Anthony Limbrick.
Grimsby are currently 18th in League Two on 20 points from their opening 17 games of the season and are six points above the relegation positions.
Wild, who is from Oldham, was appointed manager of FC Halifax in July and has made a great to life with the Shaymen. His side are currently 5th in the National League.
He played amateur football as a youngster before taking up coaching at the age of 18. He worked at the academy at Oldham Athletic for ten years before getting the caretaker manager’s job in December last year.
The Latics beat Fulham in the FA Cup in the last campaign under his guidance before he was replaced in the dugout by Paul Scholes, only to take his caretaker position back again a month later.
Wild was finally given the full-time job in March but left at the end of the season and has since taken the Halifax job. Could he return to the Football League now with Grimsby?