According to the Daily Mirror, Keane has already been offered the manager's job at Kasimpasa, a club based in Turkish capital Istanbul, but is delaying accepting the 1.4 million pound-a-year post while sounding out the Rovers.
Keane, who has had spells in charge at Sunderland and Ipswich but is now a TV pundit, fits the profile of the big name manager that Blackburn owners Venky's are looking for to win back the fans and secure a return to the Premier League.
Keane's former Old Trafford teammate Ole Gunnar Solskjaer is also eyeing the Ewood Park job, the paper added.
Solskjaer, who won the Norwegian title with Molde in his first full season with his old club, turned down Aston Villa in the summer, but does want to work in England, the paper said.
Rovers' 1995 title-winning skipper Tim Sherwood, currently on the staff at Tottenham, also features on the short-list for the vacancy. Rovers' hero Alan Shearer has also been linked with a return to Ewood Park, the paper concluded. (ANI )