The 34-year-old joined the Clarets last summer from Stoke City , but he has made just three league appearances this season.
Sunderland are currently in the Championship relegation zone and desperately need reinforcements if they are to avoid the drop.
Walters has played over 500 games during his career, most notably for Stoke and Ipswich Town.
He started his career with Blackburn Rovers and has also had spells at Bolton Wanderers, Crewe Alexandra, Barnsley, Hull City, Wrexham and Chester City.
Walters has won 51 caps for the Republic of Ireland, scoring 14 goals.