Judge ended last season on loan at Brentford and played a key role in helping them win promotion to the Sky Bet Championship.
The 25-year-old scored seven goals for Brentford after joining the club on loan in January and the Griffin Park outfit are keen to keep the Irishman on a permanent basis.
A number of other clubs are thought to have expressed an interest in Judge, but Brentford are in pole position to land the skilful midfielder.
Talks are thought to be at an advanced stage between both clubs and a deal is believed to be close to being agreed.
Judge is understood to be happy to join Brentford on a permanent deal and the move is expected to be finalised as early as next week.