The 23-year-old is said to be in the North West having a medical with a view to completing a £350,000 move in time to be eligible to make his debut this weekend.
Brown joined Norwich almost exactly a year ago, but has failed to hold down a first team place and scored his first and only goal for the club in the defeat at Burnley in October.
Preston are keen to bolster their ranks as their league position has deteriorated and they recently lost striker Patrick Agyemang to nouveau-riche Queens Park Rangers.