Milanič, who is Steve Evans' predecessor but two, spent four-and-a-half weeks at Elland Road in autumn 2014 but failed to win any of his six matches in charge.
But, after Maribor parted company with head coach Krunoslav Jurčić on Monday, the 13-time Slovenian champions announced that Milanič is "the first and only candidate" to succeed him at Ljudski vrt.
Milanič masterminded four of those title successes, as well as a further three in the national cup, during a five-year spell as manager between 2008 and 2013.
The 48-year-old recorded his highest ever win percentage (56.8) at Maribor, before a less successful stint at Austrian side Sturm Graz.
Milanič was the second manager hired by Leeds owner Massimo Cellino after Dave Hockaday, and was replaced initially by Neil Redfearn.
Uwe Rosler took charge last summer, but was replaced by Evans after winning only two of his 12 league matches.