Fulham owner Shahid Khan has made an offer, thought to be worth £900m, to buy Wembley Stadium from the Football Association.
It is understood Khan would pay £600m for the stadium and the FA will continue to run the Club Wembley hospitality business, valued at £300m.
The FA board discussed the approach at a meeting on Thursday.
"We would strive to be the best possible steward for a venue that is iconic," said Khan.
The owner of NFL side Jacksonville Jaguars added: "Wembley would return to private ownership and the Football Association would be able to focus on its core mission of developing players.
"I trust many if not most of you are also supporters of the England national teams, so I hope you welcome the potential of this becoming a reality."
Fulham coach Slavisa Jokanovic said at a news conference on Thursday that Khan told him "about his plan a year and a half ago - he's very ambitious".
BBC Sport understands selling Wembley would allow the FA to make a major investment into football at grassroots level.
But, according to the FA's latest financial results, it still owes £113m to public bodies such as Sport England, the Department of Culture, Media and Sport, plus the London Development Agency, which helped pay to build the stadium, which cost £757m and opened in 2007.
The FA said in January it would finish paying for the ground by the end of 2024.
The 90,000-seat stadium, which is the largest in the United Kingdom, has been the home for Premier League side Tottenham Hotspur this season while work on their new stadium takes place.
What about NFL matches?
Spurs also have a deal with the NFL to stage a minimum of two games a season over 10 years once their new stadium is complete.
Tottenham chairman Daniel Levy said the link-up with the NFL was a "compelling and exciting partnership".
NFL executive vice-president Mark Waller said having stadium options in London has been "critical to the NFL".
His statement added: "The potential purchase of Wembley Stadium is a further powerful sign of their commitment to the UK and their vision to help us grow the sport.
"This new relationship would allow for even greater flexibility in scheduling future NFL games in London."
Who is Shahid Khan?
Khan came to prominence in England when buying Fulham in 2013 from Mohamed Al-Fayed.
The 67-year-old was born in Lahore, Pakistan but moved to the United States at the age of 16 to study engineering and went on to become a billionaire as an automobile parts manufacturer.
Khan's current net worth is $7.2bn (£5.2bn), making him the 217th richest person in the world according to the 2018 Forbes rich list, and the 73rd richest in the United States.
Khan bought NFL franchise Jacksonville Jaguars in 2011 and they have had a deal to play "home" games at Wembley since 2013. The contract for that is in place until 2020 as the Jaguars have tried to put themselves at the forefront of the NFL links with London.
Fulham are pushing for a return to the Premier League, having been relegated to the Championship in 2014 soon after Khan's arrival, while Jacksonville had their best season for a decade, reaching the AFC Championship game before being beaten by New England Patriots.
Khan has stated that any prospective deal for Wembley will have no impact on his commitment to Fulham and the proposed redevelopment of the Riverside stand.
Khan's son, Tony, has been vice chairman and director of football operations at Fulham since February 2017, having previously advised on football operations.