The 53-year-old continues to be linked with the managerial vacancy at Oldham Athletic, where he had three years as a player in the eighties.
Bunn, who guided Town to last season’s Professional Development League II title, has been interviewed by the Latics.
Steve Evans, Stuart McCall, Neil Adams, Neil Redfearn, Ian Dowie and Uwe Rosler are other names said to be in the frame.
“I know there is interest in Frankie which has been publicly expressed,” said Huddersfield Town chief executive Julian Winter.
“People leave, sometimes when you don’t want them to, but you find a way of replacing them.
“It’s the same with staff as it is with players, you have to be ready for what is next.”
Bunn has been at Town for four years, the first two as Under 18 coach, and has also worked at Wigan Athletic, Manchester City, Coventry City and Rochdale.
He is still remembered by Oldham fans for scoring six times in a 7-0 League Cup win over Scarborough in 1989.
Bunn, whose son Harry is a Town first teamer, also played for Luton Town and Hull City.