The process is said to be "moving quick," according to sources, and the Buffalo News has reported a decision could happen by Wednesday.
At least three ownership groups submitted formal bids to buy the Bills on Monday, four people familiar with discussions revealed that information to The Associated Press. They spoke on the condition of anonymity because the sale is being conducted privately.
The other groups submitting bids were led by New York City real estate mogul Donald Trump, and a Toronto group led by rocker Jon Bon Jovi. The bids were submitted to Morgan Stanley, the banking firm overseeing the sale process on behalf of late owner Ralph Wilson's estate.
Three of the people said the estate issued purchase agreements to at least four groups, and potentially five. The other groups' identities are not known, and it's unclear if they submitted bids.
The purchase agreements are formal documents that are negotiated separately by each of the parties and Proskauer Rose, the legal firm representing the estate. The agreements are binding documents that outline the terms and conditions of the sale.
Once those agreements were completed over the past week, the only outstanding question left was for each group to determine its bid price.
The franchise was last valued by Forbes to be worth $935 million. But the sale price is expected to exceed $1 billion because NFL franchises rarely go on the block.
The Bills are on the market after Wilson, the Hall of Fame inductee and franchise founder, died in March.
Once identified, the prospective owner would be presented to members of the NFL Finance Committee, which is scheduled to meet next week. The candidate must also go through an extensive background check conducted by an NFL-contracted security firm.
The final step would be approval from three-quarters of the league's 31 other owners, which could come at league meetings next month. After that, NFL owners are next scheduled to meet in December.
Terry Pegula and his wife Kim have a net worth of more than $3.5 billion, and have the support of local business leaders and public officials because of their commitment to keep the Bills in western New York.
U.S. Sen. Charles Schumer has stayed closely involved with the sale process to ensure the Bills stay in New York.
Last week, Schumer expressed his support of Pegula in conversations with at least 10 NFL owners.
During a stop in Buffalo on Monday, Schumer said he had conversations regarding the sale process with both Terry Pegula and NFL commissioner Roger Goodell earlier in the day.
"We talked about the lay of the land. I'm not going to get into details," Schumer said. "But I believe that (Pegula) is enthusiastic about owning and keeping the Bills in Buffalo for generations."
Under the lease agreement reached in December 2012 with New York State and Erie County, the Bills are essentially locked in to playing at Ralph Wilson Stadium through the end of the 2019 season. There is a one-time out clause that would allow the team to break the agreement for just under $28.4 million in 2020.
Information from The Associated Press was used in this report.