Oldham Athletic, where he had a three-year spell as a player, are said to be considering a bid to bring him to Boundary Park.
The League I Latics are looking for a replacement for John Sheridan, who has joined Notts County.
Now 53, Bunn has just led Town to the Professional Development League II title.
His side topped the North section, then beat Sheffield United 2-1 in the play-off final at Bramall Lane.
The achievement maintained a bright record at a club he joined four years ago.
VIDEO: Frankie Bunn on Huddersfield Town's Under 21 play-off success:
The former Wigan Athletic, Manchester City, Coventry City and Rochdale coach initially took charge of the Under 18s.
Under his tutelage, they reached two PDL II play-off finals, winning the 2013-14 showpiece against Crewe Alexandra after topping the North section table.
That season, Town also made the FA Youth Cup quarter-finals.
Bunn then became Under 21 coach and has reached two more play-off finals.
In addition, his side made the semi-finals of this season’s Under 21 Premier League Cup, losing to Hull City on penalties.
Hull were one of three senior clubs former striker Bunn, whose son Harry is a Town first-team regular, represented as a player.
Birmingham-born, he began at Luton Town, playing top-flight football, before three season on Humberside preceded his switch to Oldham.
Bunn still holds a League Cup record after scoring six times in the Latics’ 7-0 home third-round win over Scarborough in October 1989.
Injury forced him out of full-time football at the end of that season.
Bunn played for non-league clubs Stalybridge Celtic and Radcliffe Borough before moving into coaching with Wigan.
After taking the reserves at Manchester City, Bunn was first-team coach at Coventry, where he worked with current Wales boss Chris Coleman.
At Rochdale, he was assistant to former Town first-team coach Steve Eyre.
Bunn’s development work will appeal to Oldham, who work to a tight budget.
The Latics, who host Town in a pre-season friendly on Saturday, July 16, finished 17th in League I.
They are seeking a sixth manager in 15 months after Sheridan’s departure followed those of Lee Johnson, Dean Holden, Darren Kelly and David Dunn.