A report by the Supervisory Commission for Serie A clubs (COVISOC) into player trading activity was carried out and submitted to soccer's federal prosecutor last year, with an investigation then launched.
However, in April soccer's federal appeals court cleared all 11 clubs under investigation, including Juventus and Napoli, and 59 individuals, amongst them former Juve president Andrea Agnelli and Napoli chief Aurelio De Laurentiis.
"The Federal Prosecutor, having examined the documents and preliminary acts of the 'Prisma' criminal investigation... has lodged... an appeal for partial revocation of the decision of the Federal Court of Appeal," the FIGC said in a statement.
The request to reopen the trial and apply sanctions concerns nine of the 11 clubs, including Serie A sides Juventus, Sampdoria and Empoli, as well as 52 of the 59 executives of those clubs.
The FIGC document requests that in a re-opened trial they be "sentenced to the penalties that will be respectively requested during the hearing to discuss the appeal before the Federal Court of Appeal".
Juventus, Italy's most successful team, is also under scrutiny by Italy's ordinary prosecutors and market watchdog for alleged false accounting.
These prosecutors have requested that its former Chairman Andrea Agnelli, 11 other people and the club itself stand trial.
Capital gains through exchange agreements have been discussed in Italy in recent years, due to the difficulty of establishing a precise market value for players included in swap deals.
The FIGC also said it had opened new disciplinary proceedings concerning Juventus and other unnamed clubs in the framework of the capital gains investigation of the 2021-22 football season.
