Evans, a life long Celtic fan who follows the club with zealous fervour, has made an official enquiry over the Socceroos' availability after being impressed with his stellar form for the Hoops his season.
Putting a series of injury setbacks behind him, the 23-year-old has scored six goals in 24 appearances in all competitions for the Hoops, and created four more.
Leeds' approach comes with Rogic in the midst of negotiations at Parkhead over extending his current contract, which expires at the end of next season.
Evans views Rogic as the man to supply the ammunition for Kiwi striker Chris Wood, who has bagged eight goals in 23 league appearances so far this season.
Should a deal be done to take him to Elland Road where Socceroos Mark Viduka and Harry Kewell once reigned, then the spin-off would reach all the way back to the A-League.
Cash-strapped Central Coast Mariners, who sold him to the Bhoys for $400,000 in 2013, insisted on a 20 per cent sell-on clause thanks to the acumen of former coach Graham Arnold, and would reap the windfall.
However, 13th-placed Leeds, who are looking to Rogic to provide the creative spark to spur a late charge towards the Championship play-off spots, will need to significantly lift their initial valualtion of the gifted midfielder to make Celtic blink.