Conte was seen heading to the parliament building in Rome where he was hammering out a final lineup to present to the president, who has rejected the populist coalition's proposed finance minister, the eurosceptic Paolo Savona.
![Vladimir Putin has dominated Russian politics for a quarter of a century [Getty Images]](data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D'http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg'%20width%3D'100'%20height%3D'100'%20data-ring-placeholder%3D'1'%3E%3C%2Fsvg%3E "Vladimir Putin has dominated Russian politics for a quarter of a century [Getty Images]")
The far-right League and the anti-establishment Five Star Movement (M5S) have yet to set up shop in Rome since scoring the most votes in Italy's inconclusive elections nearly three months ago.
Conte, 53, won Mattarella's approval last week to head what would be Italy's 65th government since 1946.
But the impasse over Savona has seen League chief Matteo Salvini digging in his heels, suggesting that a new election may be on the cards if the standoff continues.
M5S Senate group leader Danilo Toninelli told reporters Sunday that he thought Conte was "very close to finalising (the fresh lineup) this evening".
If it includes Savona, Mattarella is expected to confirm his refusal, which could prompt him to appoint a caretaker government until new elections can be held, probably in the autumn.
According to the Italian press, Mattarella wants to avoid isolating Italy within the European Union.
The 81-year-old Savona's hostility to the euro -- he says it has halved Italians' purchasing power -- has prompted a flurry of warnings from Brussels.
The impasse has rattled financial markets, with the Milan Stock Exchange closing down 1.54 percent on Friday.
The veteran economist issued a statement Sunday advocating a "different Europe, stronger but fairer". At the same time, he reiterated his opposition to the euro, likening its use to being in a "German prison".
Mattarella is also mindful of his role in appointing prime ministers and approving their cabinets, the most crucial functions of Italy's largely ceremonial presidency.
Salvini, 45, who is riding high in opinion surveys, stuck to his guns on Sunday, saying on his Twitter account that he was "in it to the end" and would "not surrender".
On Saturday Salvini pressed for a speedy resolution, saying that failing that he would prefer fresh elections.
M5S leader Luigi Di Maio, 31, for his part said he was prepared to "call it quits" barring a breakthrough in 24 hours. "We've already lost too much time," he said Saturday.
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