But analysts caution that the European Union -- anxious about the US president-elect's plans for trade tariffs and the war in Ukraine -- should not depend on the far-right prime minister as an effective or even reliable mediator.
Meloni has yet to confirm she will attend Monday's swearing-in, but the personal invite is one of several indications of the "great respect" Trump has for her and Italy, an Italian official said.
A spokesman for Hungary's nationalist prime minister, Viktor Orban, who has long voiced his admiration for Trump, denied reports he would be attending, saying that foreign leaders by tradition do not attend US inaugurations.
Meloni and Trump do not know each other well but share conservative values and have met twice since Trump's re-election in November.
Her post-Fascist Brothers of Italy party has long had ties with Steve Bannon, one of the masterminds behind Trump's initial 2016 ascension to the presidency.
And Meloni, unlike some of her peers, is friendly with Musk, the billionaire more often than not by Trump's side.
As such, some of Meloni's allies have speculated she could act as a "bridge" between the White House and Brussels.
But the nationalist premier has long been critical of the EU, leading many to question whether she would have its interests at heart.
- 'Fantastic' woman -
Meloni built a good relationship with Democratic US President Joe Biden, who praised her strong support for Ukraine since Russia launched its war in February 2022.
And she was quick to speak with Trump after his November re-election, also meeting with him in Paris at the reopening of Notre Dame cathedral.
Earlier this month Meloni visited Trump's Mar-a-Lago residence in Florida, where he hailed her as a "fantastic woman".
According to US media, the two dined and watched a documentary about a lawyer charged for trying to overturn the 2020 presidential election results in favour of Trump.
Her aides say no policy was discussed, but Trump's nominees for secretary of state, national security advisor and Treasury secretary also attended.
Meloni said afterward that she and Trump were "ready to work together" and brushed off Trump's refusal to rule out military intervention over the Panama Canal and Greenland, saying it was merely rhetoric aimed at China.
- Big vacuum -
"Giorgia Meloni has better relations with Trump than any other (major) European leader. However, I wouldn't call it a special relationship," said Teresa Coratella from the European Council on Foreign Relations.
In large part, Meloni is "filling a big vacuum in the current European debate on what to do with Trump, or to do with Elon Musk", she told AFP.
In terms of other EU interlocutors, the bloc's institutional leaders have struggled to get facetime with Trump and his incoming team.
Trump has boasted of his "great relationship" with France's Emmanuel Macron, but the two men share very different politics.
Meanwhile, Hungary's Orban has Trump's ear but is himself at odds with Brussels.
Trump has invited several European far-right politicians to his inauguration, including Britain's Nigel Farage, France's Eric Zemmour and two senior figures from Germany's far-right AfD party.
- 'Act for herself' -
Despite her history of euroskepticism, Meloni has surprised critics with her pragmatic approach to the EU since taking office in October 2022.
Yet suspicions remain, fueled by her party's vote last year against a second term for European Commission President Ursula von der Leyen.
"Meloni will not act for Europe, she will act for herself," said Nathalie Tocci, director of Italy's Institute for International Affairs.
"And if the consequence is the weakening of Europe, she doesn't really care."
Proof of this could come in Italy's support for Ukraine, a cornerstone of Meloni's premiership but which Tocci predicted could fall away if Trump decides to cut Kyiv loose.
- Is whispering enough? -
Meloni's overtures to Washington have broad support in Italy, particularly after the release of an Italian journalist held in Iran, freed earlier this month with US help.
But opposition parties have criticized Meloni's closeness to Musk, particularly after it emerged that Italy is negotiating with his SpaceX company to buy a secure communications network.
His threatened import tariffs could hit debt-laden Italy. The NATO member, which currently spends 1.57 percent of GDP on defence, would struggle to afford Trump's demand to raise this to five percent.
Ultimately, Tocci said, "if Trump thinks that it's in US interests to do something harmful to Europe, Italy included, he will do it, and there's no whispering that will prevent him".
© Agence France-Presse
