
Fisher, who inherited the San Francisco-based clothing retailer Gap from his parents, is reportedly about to offer about 250 million euros (394 million dollars) for Roma. Forbes magazine estimates Fisher's fortune at 1.5 billion dollars.
Part of his acquisition plan is to reserve the honorary presidency of the club for Franco Sensi, who bought it in 1993.
The Sensi family, who control Roma through their oil business Italpetroli, this week denied having received an official offer. In earlier statements, however, the Sensis admitted American investors were interested in the team.
Roma lie second in the Serie A, six points behind Inter Milan and are the only Italian side still vying for the Champions League, now in its quarter-final stage.
The club, which is quoted on the Italian stock exchange, won the Serie A title in 2001 and the 2007 Italian Cup.
Fisher, 46, owns the basketball team Oakland Athletics and the football side San Jose Earthquakes, both in California. In December, he acquired a minority share in Scottish side Celtic Glasgow.