A petition by Roma fans urging the owners to sell the capital club to George Soros has been signed by more than 15,000 people after reports that the billionaire financier had pulled out of talks.
Majority shareholder Italpetroli, controlled by the Sensi family, said last week it had met a representative of Inner Circle Sports, a global sports investment bank connected to the 77-year-old Soros.
Media reports have said Soros has ended talks because of a lack of progress. Lawyers working for Soros refused to comment.
Many fans believe the Sensis have taken Roma as far as they can and that new investment is the only way the club can take a step up and compete with the powerhouses of European football.
"Naturally fans like me have started to dream and hope for a great Roma like the great sides of Europe, competitive on every front. Our hope is that the Sensi family sells Roma to George Soros," read the petition, one of the 10 most active on the PetitionOnline website.
A source close to the situation said Hungarian-born Soros had offered 270 million euros and that there was a conflict between the family over whether to sell, with chief executive Rosella Sensi reluctant to do so.
The source also said shareholder Unicredit had written to the Sensis urging a sale. A spokesman told media the bank was an "interested spectator".
A joint statement on Wednesday from Italpetroli and Roma said there was no rift within the family.
"Contrary to some media reports, Italpetroli specifies that it has not received any letter from Unicredit," the statement added.
Shares in Roma fell almost 10 percent on Tuesday when rumours started about Soros pulling out but were up almost four percent on Wednesday.
Roma, who last won the Serie A title in 2001, have done well to be second in the top flight this season but have ultimately failed to keep pace with leaders Inter, who can wrap up the championship this weekend.
the club are still in the semi-finals of the Coppa Italia but were knocked out of the UEFA Champions League, Europe's premier club competition, by Manchester United in the quarter-finals.
Fans have seen how investment in Manchester United, from American owner Malcolm Glazer, has helped the club to move forward and reach this season's Champions League final.
Several other English Premier League clubs have been bought up by foreign tycoons but few sides in the rest of Europe have been targeted.
The fact that Roma have been eyed has enthused supporters and even players such as Daniele De Rossi have talked about how extra investment from a big name such as Soros could boost the club on and off the pitch.