The 46-year-old stepped down from his role with the Austrian side on Sunday, leading to speculation that he will become Dave Hockaday's successor at Elland Road.
Milanic has previously enjoyed success in his native Slovenia with Maribor, where he won nine trophies in five seasons including four league titles.
Leeds have been looking for a new boss following the sacking of Hockaday last month.
According to the Yorkshire Evening Post, Milanic has agreed a two-year contract to become the club's first foreign coach.
It is thought that Milanic will be joined at Leeds by Novica Nikcevic, who was his assistant at Graz.