Steve Kean's side were relegated to the Championship following a 19th-place finish in the Premier League last season.
Stoke City are thought to be interested in the 24-year-old, who is currently recovering from surgery to mend a groin injury.
Martin Dahlin, the player's representative, told Fotbollskanalen.se: "It is correct that Martin has handed in a transfer request. Of course he doesn't want to play in the Championship."
The Sweden international has played 88 games for Rovers since joining in 2007.
Blackburn have already lost Junior Hoilett after the influential forward opted to not extend his contract with the relegated side, while midfielder Steven N'Zonzi has also voiced his intention to leave.