Talks between Salvini and Mattarella were under way Monday evening at the president's office.
The anti-establishment, Eurosceptic parties are hoping to break two months of political deadlock that followed the general election, when Five Star won 33 per cent of the vote and The League, as part of a centre-Right coalition that has since unravelled, won 37 per cent.
Top on the list of negotiating points will be 5-Star's promise to give Italy's poorest a guaranteed income of £700 per month and League's pledge to introduce a flat 15 per cent tax rate for both individuals and businesses.
And he has never broken ranks with former prime minister Silvio Berlusconi, who a few days ago unlocked the possibility of a deal by agreeing to step back for the time being. But there is plenty they don't see eye-to eye on, including, Mr. Salvini suggested, justice reform, Italian adherence to European budget rules, investment in infrastructure and, perhaps most importantly, immigration. However, Mattarella warned over the weekend that he would not be a "pushover".
The person is expected to be from neither from the League nor M5S and will also probably be someone who will heed Mattarella's warnings against nationalism.
M5S leader Luigi Di Maio speaks to press after meeting with Italy's president.
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Nicola Sturgeon's government in Edinburgh insists that Holyrood must explicity agree to any changes before they can take effect. Speaking after the vote, he said any move to force legislation on Holyrood would break a "20 year old devolution settlement".
"We are writing what will be the government program for the next five years and it's very important for us to finalise it as best as possible, so we have asked the president for a few more days to definitively close the discussion", Mr Di Maio told reporters after meeting with Mr Mattarella.
Joshua Mahony, market analyst at IG, said: "The prospect of a deal between the Five-Star Movement and League party has done little to boost Italian stocks this morning, with a host of popular policies promising to shift the public finances back into trouble".
Candidates for Prime Minister include 71-year-old economist and university professor, Giulio Sapelli.
"It's all true. I have been contracted by both political parties and I have said I am totally willing".
"With a rocky coalition joining under the premise of imposing "short-termist" measures that are likely to ramp up Italian debt obligations, it comes as no surprise that markets are taking this "good news" with a pinch of salt".