According to The Telegraph, the club have agreed "the structure" of a £7m deal for the Croatian, as they look to add more craft and quality in the final third.
We have asked the club and Orsic's agent for comment.
The club, and chairman Alan Pace, are working hard behind the scenes and were hopeful of landing one or two new faces this week, deals which would appease the fan base, as well as bolster the squad, if they can get those transfers done before 11-59 p.m. on Monday.
Oršić, 29, netted a hat-trick against Spurs in the Europa League last March, and the winner against West Ham in the same competition this season,
He has 14 caps for his country, with one goal, and has played in his homeland with Inter Zapresic and Rijeka, with spells in Italy with Spezia, Slovenia on loan at Celje, South Korea with Jeonnam Dragons and Ulsan Hyundai, and in China with Changchun Yatai, before spending the last four seasons with Zagreb.