Rovers are understood to have made a bid - believed to be around £500,000 - for the Sweden international.
Larsson was also a target for Newcastle and the two clubs agreed a fee but the move fell through after Larsson was unable to agree personal terms with the north-east club.
Larsson is out of contract in the summer and has failed to reach agreement over a new deal with Blues.
Meanwhile representatives of out of favour Blues midfielder Michel are having talks with the club over his future.
Michel was signed from Sporting Gijon 12 months ago but has failed to make an impact.
He was a target for AEK Athens but they have since cooled their interest.
Blues manager Alex McLeish said: "I am sorry the Michel one has not worked out. But Barry Ferguson's form has been stunning and made it difficult for Michel.
"Who knows, it could have been different if he had got the nod ahead of Barry and played regular football.
"I've been involved in a few transfer dealings over the past couple of years and I'm disappointed this one hasn't worked out."