Elland Road was taken back by Leeds.
The San Francisco 49ers have an option to own 100% of Elland Road by January 24, 2024, according to the radio station.
The deal to take total ownership could be worth more than half a billion dollars.
The chairman of Aser has the option to void the deal.
If the option was not activated both parties could continue working together as they have done since the 49ers initially bought a 10% share of the club.
After buying a 50% stake in the city in January of 2017, the Italian businessman took full control of the business in May of that year.
13 years after the club were forced to sell it to reduce debts, he bought Elland Road in June of last year.
Future spending and the club's league status are some of the factors that would affect a future deal.
After 15 games, the team is 14th in the league, having finished ninth in their first season back in the top flight.
In May, Paraag Marathe, president of 49ers Enterprises, told the BBC that fans should trust the intentions of the club's American investors.
He said the 49ers' plans were "pure" and promised to make the club one of the biggest in the world.
He said they plan to keep Elland Road but increase the capacity of the stadium.
