Marrow is thought to be undergoing a medical at Ewood Park along with former Sunderland defender Matt Kilgallon.
Marrow is available on a free transfer after seeing out his contract at Crystal Palace.
The 23-year-old spent three years at Blackburn after joining from Bolton in 2008, but never made a senior appearance for Rovers.
Marrow joined Palace in 2011 after a successful loan spell at Selhurst Park, but he spent the first half of last season on loan at Fleetwood before returning to Palace in January.
Rovers boss Gary Bowyer is a big fan of Marrow having worked with him as reserve team boss and sees him as a key addition to his squad for next season.