Schopp recently extended his contract at the Austrian Bundesliga side and reportedly has a release clause valued at around £300,000.
Should the 47-year-old move to Barnsley, it will be the third successive occasion that the club has brought in someone who has managed in Austrian football.
Valerien Ismael’s previous job before joining the club last October was at LASK Linz and his predecessor Gerhard Struber arrived from Wolfsberger AC.
A former Austrian international midfielder, Graz-born Schopp - who represented Sturm Graz, Hamburg, Brescia, Red Bull Salzburg and New York Red Bulls in his playing career - has managed Hartberg since 2018.
He has also previously managed Sturm Graz’s second team and been an assistant at another Austrian side in St Polten.
To arrive at Oakwell, Schopp would have to satisfy new post-Brexit work permit rules which came into force in the UK on January 1.
Managers need to have worked for two consecutive years in what is designated as a top league or in three of the last five.
Clubs can argue for an exception if individuals do not meet that criteria.
Barnsley, who saw Ismael depart to West Brom on Thursday - after the Baggies agreed to pay £2m in compensation - begin pre-season training on Monday
The future of chief executive officer Dane Murphy remains up in the air with his contract running out this week and the American having been headhunted by Nottingham Forest.
Captain Alex Mowatt, whose deal expires later this week, is likely to be targeted by Ismael at West Brom, with several other Championship sides also interested in the 26-year-old.