The Express & Star understands Wolves are keen on landing the 22-year-old Montenegro international on a free transfer, with a view to sending him out on loan to gain more senior experience.
Sarkic has not played for Villa's first team, but he did impress during a loan spell at Scottish Premiership side Livingston in the first half of this season.
Contrary to some reports, he is not thought to have been offered a new deal by Villa, so Wolves would not be required to pay any compensation to Dean Smith's side.
Sarkic is also thought to have offers from a few clubs on the table, but Wolves are his preferred destination.
Rui Patricio is well established as the No.1 for Nuno Espirito Santo's charges, while second-choice shot-stopper John Ruddy has just signed a new one-year deal.
Andreas Sondergaard has been training with the first team as of late, too, while Will Norris – who has been on loan at Ipswich – is contracted until the end of next season.
But signing Sarkic would be a low-risk move for Wolves, with him seen as having good potential.
Born in Grimsby to a Montenegrin father and British mother, he progressed through the youth ranks at Belgian side Anderlecht before being snapped up by Villa in 2015.
Since then, he has had loan spells at Wigan, Stratford Town, Havant & Waterlooville and, most recently, Livingston.
Sarkic made 18 appearances north of the border in the first half of the campaign before being recalled by Villa in January because of Tom Heaton's knee injury.
He made his Montenegro debut last November, too, in a 2-0 victory against Belarus.