Larsson missed yesterday's derby at St Andrew's and his representatives held talks with Newcastle last week after a £1million bid was accepted by Birmingham.
The two parties failed to reach agreement but Sunderland, as revealed in Sportsmail, have made it clear they would like to negotiate a deal in the summer when Larsson is out of contract.
They may be pushed into something now if Villa harden up their interest. Villa remain keen on Blackpool's Charlie Adam, who was watched by Tottenham last week and has asked to leave.
Twin targets: Villa want Adam (left) and Larsson
Another Sunderland target, Inter Milan midfielder Sulley Muntari, has put in a transfer request.
Leeds United, meanwhile, want to take Birmingham defender Stuart Parnaby on loan. The full-back , 24, is out of contract in the summer and keen to play.
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Explore more:People: Stuart Parnaby, Charlie Adam, Sebastian Larsson Places: Birmingham, Newcastle