Bardsley's career at the Stadium of Light looked over under previous manager Paolo Di Canio, but the arrival of Poyet has seen the former Manchester United defender brought in from the cold.
Bardsley is out of contract at the end of the season.
Jack Colback is also in line for a new deal as manager Gus Poyet looks to secure the futures of those at the forefront of his side's recent revival.
Colback has been impressive since his return to the side - and Sportsmail can reveal the Black Cats turned down a £1.5million bid from fellow relegation strugglers Fulham during the January transfer window.
Colback has already turned down an initial offer from the club, but it is understood good progress has been made as both parties work towards an agreement.