Wolfsberger's Gerhard Struber is the latest manager to be linked to the vacant post at Barnsley.
The Reds have been without a manager since sacking Daniel Stendel on October 8.
They have been linked with a string of European-based coaches, and Sky Sports are now reporting they have approached Wolfsberger for permission to speak to Struber.
Wolfsberger are third in the Austrian Bundesliga, albeit already eight points behind the top two after 14 matches. They are bottom of their Europa League group despite a promising start which saw them win at 4-0 at Borussia Monchengladbach, then take a point off Roma.
The 42-year-old Austrian came through the youth coaching set-up at Red Bull Salzburg, and had two-year spells in charge of SV Kuchl and FC Liefering before moving to Carinthia.
Out-of-work German manager Jens Keller was spotted at Oakwell earlier this month having reportedly been interviewed for the role, which Gothenburg head coach Poya Asbaghi is said to have turned down. The Iranian-born manager has refused to confirm this.
Adam Murray has been in caretaker charge since Stendel was dismissed with his newly-promoted team yet to win a Championship game since the opening weekend of the season.
Murray has overseen hugely creditable draws against promotion contenders Swansea, West Bromwich Albion and Bristol City, but the Reds have lost their two matches against the other teams in the relegation battle.
On Saturday they were beaten 4-2 by a Stoke City side who quickly changed their manager, replacing Nathan Jones with Michael O'Neill, to send them back to the bottom of the Championship.
The second tier is currently in an international break, so Barnsley's next game is at Blackburn Rovers on November 23. The following Wednesday they travel to Middlesbrough, the third side in the relegation zone.