There was no immediate comment from the prime minister’s office.
Conte’s government was thrown into turmoil earlier this month when a junior partner, the Italia Viva party headed by former premier Matteo Renzi, pulled out of the cabinet in a row over its handling of the coronavirus crisis.
Although Conte survived a subsequent a confidence vote in parliament last week, he failed to secure an absolute majority in the Senate, meaning he will struggle to enact any policy agenda unless he can draw on new support.
The prime minister has appealed to centrist and unaligned Senate lawmakers to join government ranks, but few have responded so far.
Corriere della Sera newspaper said Conte wanted to get Renzi back on board and was looking to create a “government of national safety”, that would also have the backing of some moderate centre-right politicians.
Looking to put pressure on lawmakers, the main ruling parties have said snap elections, two years ahead of schedule, will be the only way out of the political impasse unless a solution is rapidly found.