Italian clubs Treviso and Zebre could be expelled from the Pro12, with London Welsh and London Scottish potentially taking their places.
The two sides have until the end of May to pay 1.5m euros owed to the rest of the Pro12 clubs or face immediate expulsion.
Alfredo Gavazzi, president of the Italian Rugby Federation, threatened to pull both teams out in 2014.
London Welsh and London Scottish have held talks about joining the Pro12.
Treviso, Zebre and London Welsh have declined to comment.
Discussions remain at a preliminary stage, though Scottish have said they are interested in a move from the English Championship.
Chairman Sir David Reid said last year his club was "open-minded".
London Welsh have been relegated from the English Premiership and will join their fellow exiles in the Championship next season.
Italian clubs were introduced to the Celtic competition in 2010, with Treviso and Aironi the first representatives.
Zebre replaced Aironi for the 2012-13 season and both teams have finished bottom of the table in every campaign.
Treviso have been more competitive, finishing the 2012-13 season in seventh place. They are 11th in the this season's table, 12 points adrift of 10th placed Cardiff Blues.