The source said that Fiorentina president Andrea Della Valle, Lazio president Claudio Lotito and Juventus CEO Antonio Giraudo were formally under investigation by Naples magistrates.
Former Football Federation president Franco Carraro, who resigned on Monday, and Juve general manager Luciano Moggi, who is at the centre of the affair, are also under investigation, the source said.
Naples public prosecutor Giovandomenico Lepore declined to give names but told reporters that 41 individuals were now formally under investigation including referees, federation officials and a journalist.
The Naples magistrates are looking into suspicions of "criminal association" and "sporting fraud".
In Italy, investigations by public prosecutors do not necessarily lead to criminal charges.
Lepore confirmed media reports that the investigation was looking into 19 Serie A matches from last season and one game from the second tier Serie B.
CHAPIONS MILAN
Six-times European champions AC Milan are among the other clubs who feature in the investigation, he said.
Fiorentina's involvement in the investigation had featured in media reports and on Thursday the club issued a statement saying they had "absolute conviction in the (club's) correct behaviour in all circumstances".
The Dalle Valle family, who own the club, "re-affirm the respect for rules and sporting values that represent the main element in the football project of Fiorentina", it said.
Lazio president Lotito had also earlier denied any wrongdoing by his club.
Top referee De Santis's involvement had been widely speculated upon and earlier this week he said that if he was called in by investigators he would co-operate fully.
"I am available for any discussions, not only with magistrates but with the sports' bodies. I don't have anything to hide at all," he told La Repubblica.
The first formal hearing of the investigation will take place on Monday in Rome when Moggi will be questioned, Lepore said.
The scandal erupted last week when newspapers published transcripts of Moggi's telephone conversations with senior federation officials regarding refereeing appointments.
