Swans boss Brendan Rogers hopes to capitalise on the situation and seal a deal for Pavone after holding talks with the free agent's representative.
But Pavone wants to find a new club as soon as possible with Barry McIntosh, his agent, urging Swansea to act swiftly.
McIntosh said: "Mariano has been left in limbo because of the Blackburn situation.
"He just needs to go to a club where he will have a chance to play and Swansea could be that platform.
"If it was just about money, he would not go to Swansea. But I'm a believer that there is more to football than just money. If the difference is only 10p elsewhere then the player will go to Swansea.
"They have Spanish players at the club, they have a British manager who speaks Spanish and has made a real effort.
"I know the area of Swansea and the club well from previous dealings.
"The player has offers from elsewhere so they must move fast, but it would be a great move for him."