Talks are taking place on Monday between Uefa and the UK government over the final, which is to be contested by Manchester City and Chelsea and due to be played on 29 May, with a decision expected in the next 48 hours.
The government placed Turkey on its travel red list last week, meaning fans cannot travel to the game, and are understood to prefer that the match be played at the national stadium.
Prime minister Boris Johnson said at the weekend: “It would be brilliant to host [the final] here if we can” and that “with two English teams in the final, it would be a great shame if fans were unable to attend”.
Uefa was surprised by the red list decision last Friday and is reluctant to move from Istanbul having already switched last year’s final from the Turkish capital.
It considers Lisbon a valid alternative venue, with Portugal on the UK green list for travel, meaning fans could attend without quarantine.
Another issue for Uefa is possible quarantine for staff and media travelling into the UK should the match be moved.
Wembley is currently scheduled to host the Championship play-off final on 29 May– one of the most important fixtures in the Football League calendar.
The EFL is understood not to want to move the match, but would enter into discussions if requested by Uefa.
A final consideration is the capacity. Uefa had been expecting a crowd of 25,000 at the Ataturk Stadium, while under rules expected to be confirmed by Johnson on Monday, only 10,000 would be allowed into Wembley.
An exemption for a crowd of 25,000 might have to be agreed if the final was to be moved to London, and there is speculation the EFL would also expect a crowd of 25,000 to be allowed into the play-off final were it be forced to change.