Knill, who made 150 appearances for the Iron between November 1993 and May 1997, has forged an impressive reputation as a promising lower league manager.
"The club are aware of increasing speculation regarding Alan Knill and a vacant managerial position at another club," said a statement by Bury on Thursday.
"The club wishes to state that currently we have nine game's left of this season and are concentrating solely on securing promotion from League Two. With nine games remaining, we wish to categorically state that Alan Knill is going nowhere."
Knill began his managerial career at Rotherham, where he ended his playing days, from January 2005 until March 2007.
He had a brief spell in Chesterfield's backroom staff before taking charge of the Shakers in February 2008.
They have been challenging for promotion to League One in every season since, and they are currently second in League Two - three points clear of fourth-placed Torquay United.