Mario Draghi said he wanted the game to be held in Italy rather than in London.
"Yes... I will try to stop the final being held in a country where infections are rising quickly," he said.
When asked during a news conference with Chancellor Angela Merkel in Berlin whether he advocated moving the final to Rome, Mr Draghi said: "I advocate that the final should not take place in a country in which the risk of infection is very big."
His comments come just days after UEFA sources refused to rule out moving the showpiece Euro 2020 games away from Wembley, with Budapest understood to be the first option if the games were switched.
However, a UK government source has said a deal to ensure the final stages of Euro 2020 are held at Wembley is on the brink of being struck between the UK Government and Uefa.
They said there had been "positive" talks with European football’s ruling body to address the issues around coronavirus restrictions.
Uefa is thought to be pushing for 2,500 VIPs to attend the final on July 11 without being subjected to the quarantine requirements that apply to other international travellers.
A UK source said "final details are being worked through" but ministers have indicated that some restrictions would remain in place.
But the football's governing body is understood to have issue with the strict Covid quarantine rules which would apply to visit fans and VIPs.
The UK recorded more than 10,500 new Covid cases and five further deaths in the 24 hours to 9am on Monday, according to the latest update on the government’s Covid dashboard.
In contrast, Italy recorded 495 new cases of Covid in the last 24 hours, and 21 more deaths from the virus, its health ministry confirmed.
Boris Johnson says they will talk to UEFA but his priority is keeping the country safe:
On Friday, Prime Minister Boris Johnson said his "priority" was keeping the "country safe" but said the government would talk to football's governing body UEFA and see if "sensible accommodations" could be made.
He added: "We’ll do what we have to do to keep the country safe from Covid.
"That’s obviously going to be our priority and we’ll be talking to UEFA about what they want and see if we can make some sensible accommodations but the priority obviously has to be public health."
Budapest would be an attractive alternative option for UEFA, where matches are being played at 100% capacity at the Puskas Arena.
The British government confirmed the final four Euro 2020 matches at Wembley could be played in front of crowds of at least 40,000 despite the decision to delay the final easing of coronavirus restrictions.
The games will be part of the government’s Events Research Programme (ERP) which has been running since April and has been used to test various ways to get fans back into venues without the need for social distancing.