CVC is in talks to buy a 20 percent stake for 2 billion euros ($2.17 billion), valuing the league at 10 billion euros, the newspaper reported citing two people briefed on the discussions, which began at the end of last year.
Blackstone is separately considering lending to clubs to help cover their costs during the shutdown of fixtures, the report added, citing people familiar with the proposal.
Blackstone declined to comment when contacted by Reuters.
CVC and Serie A did not immediately respond to Reuters requests for comment.
The talks are at an early stage and there is a potential legal hurdle, the report said, citing one person with knowledge of the proposal.
The deal could give CVC, which has had sports deals in the past, a role in selling broadcasting rights for 10 years from 2021, the report added citing sources.
Last year, CVC had held talks with soccer's global governing body FIFA on acquiring the commercial rights to the revamped Club World Cup.
On March 9, Italy suspended the league campaign as part of a nationwide lockdown and the country's sports minister said it is unlikely to resume the league championship because of the COVID-19 epidemic.