"It's coming down the backstretch," the person said, speaking on the condition of anonymity because the sale is being conducted privately.
The timetable was pushed back about a week because Morgan Stanley, the banking firm overseeing the sale on behalf of late owner Ralph Wilson's estate, extended a deadline last month in an attempt to increase the number of prospective bidders.
A new owner is still expected to be identified by October, but it's not certain whether it will be in time to be approved by NFL owners at league meetings in early October. And that approval would come only after the prospective candidate's background and finances are vetted and approved by the league's finance committee.
The Bills are for sale after Wilson died in March.
Buffalo Sabres owners Terry and Kim Pegula are considered the front-runners among a small group of candidates who have already met with members of Wilson's estate over the past two weeks.
Pegula was last valued by Forbes to have a net worth of $3.3 billion, and that was before he sold 75,000 acres worth of drilling rights for $1.75 billion two weeks ago. He also has the backing of a majority of Buffalo public and business leaders because he is committed to keeping the Bills in western New York.
New York City real estate developer Donald Trump is also a contender, and met with Wilson's estate two weeks ago.
Questions remain regarding the status of several other prospective ownership groups.
Former Sabres owner Tom Golisano submitted a non-binding bid after Morgan Stanley extended its deadline.
But Golisano has not yet met with Wilson's estate, two people familiar with the process told The AP.
The meeting is regarded as important for prospective buyers to begin formulating their bids. The daylong meeting includes a lengthy presentation and access to hundreds of pages of documents outlining the Bills' financial information.
A Toronto-based group led by rocker Jon Bon Jovi has met with Wilson's estate, but has encountered several setbacks over questions regarding its intentions of keeping the Bills in Buffalo.
Two people familiar with discussions confirmed to The AP that a group headed by Bills Hall of Fame quarterback Jim Kelly turned down Bon Jovi's request to join forces last week.
The Buffalo News first reported that development last weekend.
Under their lease that runs through the 2022 season, the Bills are essentially locked into playing at Ralph Wilson Stadium through the 2019 season. There is a one-time exception that would allow them to break the agreement for just under $28.4 million in 2020.
A letter Bon Jovi had published in the newspaper two weeks ago was also received with skepticism by Bills fans and officials.
He didn't state in the seven-paragraph letter that he was committed to keeping the franchise in Buffalo. The only commitment Bon Jovi provided was working with state and local officials to identify a site for a potential new stadium.
His group is rounded out by Larry Tanenbaum, chairman of Maple Leaf Sports and Entertainment, and the Rogers family which controls Rogers Communications.
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