Jon Dahl Tomasson is looking to add an experienced defender to the mix at Ewood Park and is keen on Batth.
Blackburn have been hoping that they could snap up Batth on a cut price deal this summer, but Sunderland have not played ball.
And it is suggested that it is now hugely unlikely that Blackburn will land the Black Cat this summer.
Sunderland landed Batth from Stoke City in the 2022 January transfer window on a free transfer.
He played regularly for Sunderland over the course of last season as the Black Cats booked a spot in the Championship playoffs.
However, the 32-year-old will not be offered an extension to his Sunderland deal when it expires next summer.
Batth is a hugely experienced Championship campaigner and has made 300 appearances in the second tier, picking up 44 bookings along the way and being sent off just once.
