Matteo Salvini, head of the nationalist League, had earlier said in a statement that he and Five Star Movement (M5S) leader Luigi Di Maio were "writing history" and would call President Sergio Mattarella to announce a new agreement.
Press agency AGI reported that Mr Di Maio made a brief call to the president's office to "announce that they are ready from [Monday] to report on everything, including the name of the prime minister".
If the head of state accepts the nomination, the position could be filled within days.
Following a second day of negotiations with Mr Salvini in Milan, Mr Di Maio said the prime ministerial candidate will be "a politician and not a technician".
According to Italian media reports, the nominee will be a "third party" belonging to neither the League or the M5S and would have international authority.
Mr Salvini and Mr Di Maio are scheduled to meet again in Rome on Monday before being received at the Quirinal, the presidential palace.
Around 70 days after the legislative elections that failed to produce a clear parliamentary majority, it would appear that the League and the M5S have found some common ground to form the first anti-establishment government in Italy and western Europe.
According to reports, the parties have agreed on rolling back increases to the age of retirement, while the M5S is willing to follow the League's hardline anti-immigration policies.
Mr Salvini and Mr Di Maio are also willing to make compromises over their flagship policies - the League's drastic drop in taxes and the M5S's universal basic income - which look tricky to reconcile in the eurozone's second most indebted country.
The most sensitive issue is undoubtedly that of immigration, and according to Italian daily Il Corriere della Sera, "the approach of the League is more muscular than that of M5S".
For the composition of the government, the League and M5S must also agree on representation from the parties.
On its own, Mr Salvini's League won 17 per cent of the votes on March 4, but it was part of a right-wing alliance including Silvio Berlusconi's Forza Italia (FI) party that garnered 37 per cent of the vote.
M5S is by far Italy's largest single party after conquering nearly 33 per cent of the electorate.