The Scottish champions will move to extend Rogic’s current contract following an approach from Leeds for the Australia international.
Rogic, 23, is a major target of Leeds and the club have been lining up a bid for him in the past few days.
United are understood to value Rogic in the region of £1m but the youngster has been central to Celtic’s season and is in line to receive a contract extension.
Rogic’s existing deal expires in June 2017 and sources in Glasgow say Celtic manager Ronnie Deila is reluctant to lose a player who has established himself as a first-team regular.
Celtic paid around £400,000 to bring Rogic to Scotland from Australian club Central Coast Mariners in January 2013.
The attacking midfielder was troubled by injury in his first two-and-a-half seasons and spent time on loan at Melbourne Victory but has featured heavily in Celtic’s current league campaign.
Evans is believed to see Rogic as an out-and-out number 10 but Celtic’s plan to lengthen his contract could now spell the end of United’s interest.