Reports are the prospective buyer is billionaire owner of Fulham Football Club, Shahid Khan, who also owns the Jacksonville Jaguars NFL team.
It is understood the approach includes £500m for the stadium and £300m for the FA to keep the Club Wembley debenture and hospitality business.
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.”
The 90,000-seat stadium, which is the largest in the United Kingdom, cost £757m to build and opened in 2007.