Roma, controlled by U.S investors, had set a March 14 deadline for prospective partner Sheikh Adnan Adel Aref al Qaddumi to come up with the funds needed to invest in the club.
In a statement on its website, Roma said the deal had not been concluded and that a preliminary agreement with al Qaddumi announced last month had been terminated.
Little was known of al Qaddumi, with Italian media reports saying he was born in Jordan but had lived in Italy for the past two decades and questioning how wealthy he was.
Money from Qatar and Abu Dhabi respectively has helped turn Paris Saint-Germain and Premier League champions Manchester City into major players on the European football scene in recent years.
Roma, who are seventh in Serie A, last won the Italian title in 2001 but have ambitions of competing with the best in Europe.
"While it is unfortunate that this transaction did not close, it will not impact the health of the team," the club said in the statement.
Roma added that they would work with Italian bank UniCredit, which has a stake in the club, to meet their funding needs.
"We look forward to building on our initiatives to enhance the team's brand, including the construction of a world-class stadium in Rome and the team's exciting new partnership with Nike," the club added.
Roma share the publicly-owned Olympic Stadium with city rivals Lazio but hope to move to a new ground by 2016 to boost their revenues.
They agreed a 10-year kit supply deal with U.S sportswear giant Nike this week that will begin from 2014/15 and should help the club gain greater international exposure.
