Quite when the bid was made is unclear but news of it follows hot-on-the-heels of Blues bid for Rovers top scorer Paul Dickov.
Savage has been linked with a move to Blackburn ever since Mark Hughes, his former Wales international boss and Mark Bowen, his former coach at St Andrew's, took over at Ewood Park back in October.
No confirmation of the bid has been made by either club as yet but it is unlikely Blues will allow Savage, who signed a three year contract extension in the summer, to leave during the transfer window in January.