The centre-back began his career at Luton before moving to West Brom in a £2.5m deal in July 2007.
Barnett then progressed to Norwich in January 2011 but found his chances there limited last season.
The 27-year-old played just 11 times for Chris Hughton's side before being loaned out to Cardiff.
Barnett played eight times for the Welsh club, helping them secure promotion to the Premier League.
He subsequently returned to East Anglia but now appears to be surplus to requirements.
Barnett could now be snapped up by new Wigan boss Owen Coyle as he seeks to guide the club back to the top flight at the first attempt following their relegation last season.