Norburn has impressed for Rovers this season after arriving at the Memorial Stadium last summer from Leicester City.
The 20-year-old has quickly established himself as a key player for Rovers and he has been instrumental in the surge up the League Two table in recent weeks.
Norburn's performances for Rovers have not gone unnoticed by teams higher up the football league with scouts flocking to watch the talented midfielder in action.
Championship duo Barnsley and Peterborough and League One hopefuls Doncaster Rovers are all thought to be keeping tabs on Norburn.
Rovers are keen to keep hold of Norburn, but they could face a fight to keep hold of him in the summer if his suitors step up their interest.