Creditor bank UniCredit has been working with owner Italpetroli for months in an effort to put the club up for sale and wipe out large debts.
"It went well, there has been a kick off," Fiorentino told reporters after a meeting on Monday with sale advisor Rothschild.
He said the sale process had begun with the agreement of Italpetroli head and club president Rosella Sensi and that UniCredit, which has de facto control of the club, was interested in a good result rather than a speedy sale.
Russian media reported on Tuesday that the vice president of oil company LUKOIL, Leonid Fedun, was interested in purchasing a controlling stake, but LUKOIL had no comment.
Italian media have listed several other interested parties.
Roma shares were up 10 percent at 1.210 euros at 12:09pm GMT.
Roma, who finished second in the Italian league last season and were runners-up in the Italian Cup despite their financial constraints, have been the subject of continual takeover talk with Italpetroli struggling to deal with arrears.
Creditors have been trying to force a sale for three years but bids from billionaire financier George Soros and a Swiss consortium never came to fruition.
Italian pharmaceutical magnate Francesco Angelini has never put forward concrete plans for a bid after saying he wanted to buy a majority stake in the club.
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