Citing government sources, the paper said the government could sell 51% of ITA, the successor to Alitalia, to Lufthansa for 250 million euros ($261 million) and 29% to FS, while the rest would remain with the Treasury.
Lufthansa and FS declined to comment. The Italian Treasury could not immediately be reached for comment.
Through a tie-up with ITA, FS could exploit synergies between air and rail transport, especially with the high-speed services its runs connecting major cities in Italy, the paper added.
Rome has been keen to sell a majority stake in the airline and retain a minority, non-controlling stake in the initial stage, but the privatisation has proved difficult.
The government reopened the process at the end of last month after an exclusivity period for talks with U.S. private equity fund Certares, Air France-KLM and Delta Air Lines failed to produce a deal.
Shipping group MSC, which had partnered with Lufthansa earlier this year to bid for ITA, said earlier this week it was no longer interested in the transaction. However, Lufthansa is still keen on buying into ITA, a spokesman for the German carrier said last week.
($1 = 0.9586 euros)
(Reporting by Agnieszka Flak in Milan, Giuseppe Fonte in Rome and Ilona Wissenbach in Frankfurt; editing by Jason Neely)