The 23-year-old midfielder is emerging as one of Steve Evans’ major January targets after a long run in Celtic’s starting line-up this season.
Rogic - a player who Leeds see as a natural number 10 - has re-emerged at Celtic Park on the back of two-and-a-half mixed years in Glasgow.
The Scottish Premiership champions paid £400,000 to bring Rogic to Scotland from Australia in January 2013 but his initial impact was restricted by injury and Celtic sent him on loan to Melbourne Victory in 2014.
He has started all but three of Celtic’s league matches this season, however, and scored five goals.
Evans refused to comment on Rogic when contacted by the YEP but Leeds are understood to value him in the region of £1m.
United have so far completed two deals in the January window, landing Liam Bridcutt on loan from Sunderland and Mustapha Carayol on loan from Middlesbrough, but Evans said last week that he was looking for as many as three more recruits.
Rogic spent his earliest years in the Australian leagues and was playing for Central Coast Mariners when Celtic moved into sign him. He has been capped 13 times by Australia’s national side.