Local media on Sunday suggested that Rome would have to push back the deadline for bids, perhaps until after European elections.
Italian state railway operator Ferrovie dello Stato and US carrier Delta Air Lines are prepared to contribute to a new rescue bid worth around €1 billion, but there is still a shortfall of around €400 million.
Alitalia was placed under special administration in 2017 after workers rejected the latest in a long line of rescue plans, and Ferrovie has been struggling to find partners ready to inject fresh funds and revamp the airline.
Speaking on the sidelines of a conference in Warsaw, Di Maio said the government had received no formal bids for Alitalia from motorway operator Atlantia, infrastructure company Toto Holding or any other groups.
“We’ll see in the next few days if there are any formal bids,” he said.
The Italian government has granted Alitalia a €900 million euro bridging loan that will expire at the end of June.