Draghi resigned on July 21 and his key ministers have been debating whether the sale process can go ahead with a government acting in a caretaker capacity ahead of a snap national election scheduled on Sept. 25, sources told Reuters.
"Everything can change following the vote and the relaunch of our national airline will be the responsibility of whoever governs," far-right Brothers of Italy party leader Giorgia Meloni said in a statement.
Draghi's office declined to comment.
The Treasury planned to privatise ITA through a direct sale while retaining a minority, non-controlling stake in the initial stage. The original goal was to clinch a preliminary deal with the potential buyer by the end of June.
Rome must decide with which of the two consortia competing for Ita Airways to start exclusive talks.
Before the political crisis erupted last month, shipping group MSC, which is working with Germany's Lufthansa, was seen as the leading candidate, sources have previously said.
The two groups are facing a rival bid made by a consortium comprising U.S. private equity fund Certares, Air France-KLM and Delta Air Lines Inc.
While the privatisation process is set to become a contentious matter in the electoral campaign, Ita Airways last week asked the government for 400 million euros ($409 million) in fresh capital, following a first tranche worth 700 million euros paid by the Treasury last year.
Under the terms agreed with the European Union, Rome can inject up to 1.35 billion euros into the carrier by 2023.
With an additional 250 million euros due next year, a privatisation deal would potentially reduce the financial support granted by the state, limiting the costs for Italian taxpayers.
However, Meloni suggested her party could change course should it emerge as the largest single party in the next parliament.
"We need to carefully evaluate the state's presence in the carrier and equity partnership with other carriers," Meloni said.
($1 = 0.9789 euros)
(Reporting by Giuseppe Fonte; Editing by Keith Weir)
By Giuseppe Fonte