Caretaker boss Chris Brass said he was in no rush to decide on his future after Bury shocked Championship side Norwich 2-1 in their FA Cup replay.
Brass took charge of Bury for the first time on Tuesday evening
Brass currently combines a job at the Shakers' centre of excellence with playing part-time for Hyde United.
He was only named as temporary boss on the morning of the match, and said: "It was a tough decision to take - Hyde have been more than patient.
"But there's no timescale. The board have to decide what they want."
Bury sacked manager Chris Casper and director of football Keith Alexander on Monday, placing ex-York manager Brass in charge the following day.
Brass added: "I've explained the situation to Hyde, and someone from Bury has touched base with them.
"If I'm given the opportunity here, I've got a major decision to make as opportunity doesn't always knock twice.
"But it's just nice to put a smile back on everyone's faces.
"It's been a tough few days and I have a lot of respect for Chris Casper."