The non-exclusive deal is fully financed but not signed, meaning another group could still come in and buy the team. Any deal also has to be submitted and approved by league owners.
A group led by Canadian billionaire Steve Apostolopoulos is still involved in the sales process, a source told ESPN.
The group led by Harris, co-owner of the Philadelphia 76ers and NHL's New Jersey Devils, continues to be optimistic that it will get the team. That group includes basketball legend Magic Johnson.
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No deal has been signed, sources told ESPN and any deal has to be submitted and approved by league owners.
Tilman Fertitta, the owner of the NBA's Houston Rockets, told CNBC on Wednesday that he bid $5.6 billion -- the value Forbes placed on the franchise -- and was not going to go higher than that.
A spokesperson for the franchise said the team was not in a position to comment. The NFL declined to comment.
The current record sale for an NFL franchise, set in August, is $4.65 billion after a group led by Walmart heir Rob Walton bought the Denver Broncos.
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A deal likely wouldn't be approved until the next league meetings, scheduled for May 22-24 in Minneapolis. The NFL's eight-member finance committee will examine the documents and then put the sale to a vote of the other 31 owners. The NFL is familiar with Harris, who was a finalist in the bidding for the Broncos last summer before the Walton group won out.
If the expected deal is approved, Harris would own controlling stakes in teams in three of the four major North American pro sports leagues. He and David Blitzer have owned the NBA's Philadelphia 76ers since 2011 and the NHL's New Jersey Devils since 2013.
Harris has owned a piece of the Pittsburgh Steelers, which he needs to sell before he could buy the Washington team.
The deal for the once-proud Redskins organization, now redubbed the Commanders and mired in years of football mediocrity, would also include FedEx Field in Landover, Maryland, as well as the team's practice facility in Ashburn, Virginia.
For any new owner, the biggest immediate challenge for the long-term future of the organization is a new stadium to replace FedEx Field, the rushed-to-completion home of the team since 1997 in Landover, Maryland, that has not aged well. Virginia abandoned a stadium bill last spring given the number of off-field controversies swirling around the team.
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The team finished 8-8-1 last season under coach Ron Rivera, entering his fourth year in charge.
Getting fans back is a major priority after Washington ranked last in the league in attendance in 2022 and was second-last in 2021. The team rebranded last year as the Commanders after dropping the name Redskins in the summer of 2020, upsetting many fans -- including members of Indian tribes -- and going by the Washington Football Team for two seasons.
Snyder bought his boyhood team in 1999 for $750 million and despite mounting criticism repeatedly said he'd never sell. That changed after multiple investigations by the league and U.S. Congress into Washington's workplace misconduct and potential improprieties. The congressional investigation found Snyder played a role in a toxic culture.
Indianapolis Colts owner Jim Irsay in October became the first to suggest there was "merit to remove" Snyder, a nearly unprecedented move that would have also taken a three-quarters majority to happen. Instead, two weeks later, Snyder and his wife, Tanya, hired Bank of America Securities to explore a possible sale of the team.
The news was first reported by Sportico.
ESPN and The Associated Press contributed.