Boris Johnson has offered to stage the whole of the delayed tournament which was due to take place last summer across Europe.
And reports suggest that the Prime Minister’s plans have been well received by European football bosses.
Wembley is already due to stage seven games at the tournament, which will now take place this summer.
The seven fixtures include all three of England’s opening group matches, both semi-finals and the July 11 final.
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As well as Wembley, Euro 2020 fixtures are due to be played at Hampden Park in Glasgow, Dublin, Amsterdam, Bilbao, Bucharest, Budapest, Copenhagen, Munich, Rome, St Petersburg, and Baku.
However, UEFA wants each host country to commit to allowing fans into stadia for the games.
As it stands, only nine cities have been able to commit to Covid restrictions being eased.
But England – pending UEFA approval – could come to the rescue and host the tournament in full if the vaccine rollout is successful.
And national reports in The Sun suggest that Sunderland’s Stadium of Light and Newcastle United's St James’s Park would be among the stadiums chosen to host matches.
Old Trafford and the Etihad Stadium are also on the list alongside Anfield, Villa Park, Wembley, the Tottenham Hotspur Stadium, the Emirates and the London Stadium.
Missing from the list, though, is Sheffield Wednesday's Hillsborough Stadium – which was used when England hosted Euro 96.
Leeds United's Elland Road also doesn't feature with the Whites’ relaying their pitch this summer.
A decision on the Prime Minister's proposals for the tournament to be hosted in England is expected in April.
However, The Times reports that the FA and UEFA believe that plans are logistically too difficult to push through.
The Stadium of Light has played host to four England international matches previously, the most recent coming five years ago as the Three Lions defeated Australia 2-1 in a friendly.
Sunderland’s stadium also saw the national team defeat Belgium in a friendly back in 1999, with England’s under-20 team also using the Stadium of Light three-years later in a 5-2 defeat to Italy’s under-20 team.
England then played two Euro 2004 qualifiers at the Stadium of Light in 2003, defeating Turkey and Slovakia 2-0.