The Whites made an initial approach earlier this summer, which was reportedly rejected by the Italian giants. The Slovenian has yet to make his debut for Milan but has featured heavily for their U19 side.
Benedicic is a Slovenia U21 international who usually plays as an attacking midfielder, something that United desperately lack at present.
Fellow Serie A youngster Federico Viviani is reportedly close to joining Leeds on loan, with the duo set to give Leeds the creative spark they need for the upcoming Championship season.
Speaking to La Bottega del Calciofilo, Benedicic said:
"We are waiting for all of the documents and the last confirmations, then I will sign. I am at one step away from becoming a Leeds player.
"[My goal is] to achieve a place in the starting eleven."
While Benedicic has told Giulianelli he is close to joining the Whites, Phil Hay has been told that a deal is still to be agreed.
Zan Benedicic hasn't signed yet but is a real option for Leeds. His agent says the two clubs are still discussing a deal atm. #lufc— Phil Hay (@PhilHayYEP) July 28, 2014
The YEP have also been told that Bologna striker Robert Acquafresca isn't wanted by Cellino despite reports from Giulianelli.
If both midfielders could complete their deals before the end of the week, it would give Leeds a big lift going into the clash against Milwall, although the first fixture may come too soon for the pair.
United have failed to inspire so far during pre-season and the club need to make a number of signings to get the fans on board before the season gets underway.