Ministers are reportedly discussing a plans to exempt Uefa and Fifa officials, politicians, broadcasters and sponsors from having to self-isolate on arrival to stop the location change.
This would come despite concerns that such a decision may lead to a rise in Covid infections, and provoke a public backlash.
But Prime Minister Boris Johnson is said to be drawn to the plans on the condition that they would boost a joint Home Nations bid for the 2030 World Cup.
About 2,500 designated VIPs attending games at Wembley would not have to abide by quarantine restrictions on travellers under the plans, The Times reported.
They would be allowed to attend matches at Wembley during the knockout phase of the tournament, as well as training sessions and meetings with the UK government.
Ministers are concerned, the paper reported, that if they do not relax the rules the semi-finals and final will be moved to Hungary.
The country will have no border restrictions for travel within the Schengen zone from next week, and would host games with full stadiums.
Home Office minister Kit Malthouse stressed that the UK wanted the tournament to carry on “as close to normality as possible”.
Apart from England, Scotland and Wales, and Turkey which is on the Red list, every team competing at the national tournament is on the amber list
Up to ten days’ isolation is needed for those returning from amber and red destinations.