Webber has been linked with a move to Norwich City.
He joined the Terriers in 2015 from Wolves, for whom he was head of recruitment.
Before that he worked in the same position at Premier League outfit Liverpool, and has had spells in the backroom staff at QPR and Wrexham.
Championship side Huddersfield Town have placed head of football operations Stuart Webber on gardening leave after he expressed a wish to leave.