The media outlet claim Town's head of football operations is the frontrunner for the newly created role, having transformed the club's scouting operation.
Webber, who was linked with the Rangers director of football role earlier this month, is the favourite of the board with PA claiming a deal could be done in the next few days.
The Huddersfield Town man was previously head of recruitment at Wolverhampton Wanderers and, before that, spent three years as director of recruitment at Liverpool FC, helping sign a 15-year-old Raheem Sterling.
In a behind the scenes shake-up at Carrow Road, the Canaries have made the chief executive role redundant with the role expected to help find a new manager after Alex Neil was sacked 10 days ago.
Huddersfield Town have refused to comment on media 'speculation' at this current time.