The forward looked set to move to Blackburn Rovers until Steve Kean's men pulled out of the deal late on.
Pavone has been linked to Liverpool and Fulham, but it looks like Swansea are in pole position for his signature after talks between the club and agent.
The 29 year old ended the season at River Plate, on loan from Real Betis, but he couldn't stop the club from dropping down to the second tier of Argentine football.
After paying up his contract at Betis, Pavone is available on a free transfer.
"Mariano has been left in limbo because of the Blackburn situation," his agent Barry McIntosh told the Mirror.
"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."