Shelly Sterling and her lawyers have been negotiating with the NBA since commissioner Adam Silver banned her husband from the NBA for life on April 29 for making racially charged comments on an audiotape.
Although the league has yet to accept this arrangement, sources said that if she is willing to sell the entire team with terms that are acceptable to the league, this could bring a startlingly quick end to what appeared to be a protracted legal battle.
Heat star LeBron James said it was "very important" a resolution be reached quickly.
"We don't want this lingering around our sport," he said. "It sucks that it happened. The players and owners and everyone associated with this game knows there's no need for it. So the quicker it gets done, the quicker we can move on."
James said that Sterling selling the team was "the way it should be."
"He shouldn't be part of this league," James added.
Shelly Sterling does intend to sell the Clippers, but it remains unclear how much of a share -- if not all -- she's willing to sell, according to a source with knowledge of the situation. Sources said the only way the NBA would accept the terms of this agreement between Donald Sterling and his wife would be if the team was sold in its entirety.
Among the issues Shelly Sterling is considering, the source said, are the substantial tax obligations she would incur from the sale.
According to IRS rules, the Sterlings would have to pay a federal long-term capital-gains tax of 20 percent and a California tax of 13.3 percent. The tax would be on the difference between what the team was bought for and what it is ultimately sold for. If the team is sold for $1 billion, the Sterlings would be taxed $328.5 million on the sale. Sterling bought the team from Irv Levin in 1981 for $13.5 million.
In addition to the lifetime ban, Donald Sterling was fined $2.5 million by Silver after the release of a TMZ recording in which he told a female friend, V. Stiviano, not to bring black people to Clippers games.
The NBA filed charges to terminate Sterling's ownership of the Clippers this week. He has five business days -- until Tuesday -- to respond to the charges. A hearing was set for June 3 in New York, with a vote of the board of governors to take place thereafter.
The league was still set on the previous course despite news of the potential sale.
Said NBA spokesman Mike Bass in a release: "We continue to follow the process set forth in the NBA Constitution regarding termination of the current ownership interests in the Los Angeles Clippers and are proceeding toward a hearing on this matter on June 3."
Sterling's lawyer, Max Blecher, responded to the charges by asking for a three-month delay. That request was immediately turned down by the NBA, sources said.
Blecher indicated in his email to the NBA that Sterling intended to fight the charges and the move to terminate his ownership, saying he did not believe he'd done anything to deserve such punishment.
But a source said that over the course of this week, Sterling has rethought his position and formally agreed to allow Shelly -- an alternate governor of the team -- to negotiate a sale.
NBA rules, however, prevent him from transferring a controlling interest in the team to anyone, even an alternate governor. A new controlling owner would need to be approved by the board of governors, and Shelly Sterling would not be approved.
Although Shelly Sterling's lawyers have made it clear to the league that she intends to maintain her 50 percent interest in the team, they have also said both publicly and privately that she would like to resolve the situation amicably.
The agreement between Donald Sterling and his wife was first reported by TMZ.
ESPN.com's Michael Wallace and Darren Rovell contributed to this report.
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