The Hammers have been long-term admirers of Hadzic and Sturm Graz are reportedly looking to cash in on their interest now.
Hadzic can play as either a centre-back or a defensive midfielder and could provide decent cover for West Ham as they look to add depth to their squad in January.
Sam Allardyce's men are aiming to strengthen their bid for a Champions League spot by bringing in additions to bolster their squad in the coming month and Hadzic appears to be an option for the London club to pursue.
The 25-year-old, who was part of Bosnia's World Cup squad, has played his entire career to date in Austria and his technical ability has stood out.
He would be required to make a big step up if he were to move to the Premier League, but West Ham clearly have some belief that he would be able to make the grade.
The Hammers have already been active in the transfer window, signing Doneil Henry from FC Toronto and allowing Mauro Zarate to leave to join Queens Park Rangers on loan.