Rovers have quelled interest from Sunderland's North East neighbours Middlesbrough, turning down bids in excess of £12million for the Scotland international striker.
Rovers were not keen on selling their prized asset to a rival Championship club and are ready to do business at a lesser fee with Sunderland - who could yet send players in the opposite direction.
However, Financial Fair Play rules - which Blackburn are currently governed by, mean no deal for Rhodes can include players, but they could be sent on loan in separate deals, even if they were a direct result of that transfer - but Rovers in the end would prefer straight cash.
And although Sunderland are unlikely to go as high as Boro, they will come close to £12million, which is likely to be enough to see a deal done.
Sunderland endured a torrid start to the new Premier League season with a heavy defeat at Leicester City, and Dick Advocaat wants to bring in at least another three new faces before the summer transfer deadline passes.