Sky Sports understands Barnsley number two David Flitcroft has turned down the chance to take charge of Bury.
As Sky Sports revealed earlier this summer, former Bury player Flitcroft emerged as one of their leading targets as soon as Richie Barker left for Crawley Town.
Flitcroft, though, has pledged his future to Championship side Barnsley and manager Keith Hill - where the duo have earned a lot of praise for their work since taking charge last summer.
Bury have had Peter Shirtliff as caretaker boss all season, but he has been ruled out of the job having failed to win a game so far this term.
But the club have confirmed that both Shirtliff and coach Ben Futcher would be remaining as part of their new managerial set-up.
Bury hope to make an appointment this week.