The Tykes have reportedly been given permission to speak to the former Cheltenham and Burnley player, who made over 600 professional appearances before moving into management.
The 44-year-old was born in Belfast but grew up in Beadle, North Yorkshire and has one year left on his contract in the Jonny-Rocks Stadium.
Last season, Duff guided Cheltenham to their first-ever automatic promotion in the EFL, as they won the League Two title ahead of Cambridge United and Bolton Wanderers.
He has oversaw 82 wins, 60 draws and 61 defeats in 203 games.
His appointment would represent a change in direction from Barnsley, who have adopted a policy if appointing coaches from overseas in recent years.
The shortening of odds on Duff's appointment has also saw the prices lengthened on other contenders.
Next Barnsley manager odds (correct as of 11pm, May 20, 2022)
Michael Duff 1/1
Martin Devaney 10/1
Mick McCarthy 14/1
Jimmy Floyd Hasselbaink 16/1
Neil Warnock 16/1
Chris Beech 25/1
Joey Barton 25/1