Daily MF said in an unsourced report that CDP taking a stake in Atlantia could be an alternative to the revocation of the toll-road concession which the government is considering after last year a bridge collapsed on a motorway operated by the group killing 43 people.
Prime Minister Giuseppe Conte said on Monday he expected a government decision on the matter by the end of the year.
Shares in the group controlled by Italy's Benetton family have lost 10% of their value over the past month.
It was not immediately possible to obtain a comment from CDP.
(Reporting by Valentina Za)