The investigation concerns the 2013 failure of Chil Post Srl, a newspaper distribution and advertising company headquartered in Genoa, of which Renzi senior was the chief executive, Il Secolo XIX reported.
The case was opened in September 2014 but the public prosecutor had since asked that it be dismissed.
On Monday, preliminary hearing judge Roberta Bossi rejected the request, saying that there would need to be further investigation to ascertain if criminal activity had taken place.
“Further investigation is needed to establish the contractual relations that existed between Chil Post Srl, Chil Promotion and the TNT group,” Bossi said.
Speaking after the judge's decision, Renzi's defence lawyer, Federico Bagattini, remained upbeat.
“The investigation won't turn up anything surprising,” he said. “Everything can be proven by documentation and paperwork.”
Should the case go to trial it will no doubt be highly embarrassing for the premier, who has frequently spoken of the need to rid Italy of corruption.