Sports Illustrated first reported the letter from Maxwell Blecher. The contents were confirmed by the person who spoke to The Associated Press on the condition of anonymity.
Blecher, a prominent antitrust attorney, acknowledged sending a letter but would not discuss its contents Friday.
NBA Commissioner Adam Silver banned Sterling for life and imposed the fine following the release late last month of a recording in which Sterling makes racist remarks. Silver also called on owners to oust Sterling from the league, which would require a three-fourths vote among the league's 29 other controlling owners.
"We regard the dispute between Sterling and the NBA to be a private matter," Blecher said. "We do not intend to have a trial in the press."
Blecher said he has known Sterling since the early '80s, when he helped resolve a dispute that allowed the Clippers to move from San Diego to Los Angeles. Sterling has owned the Clippers since 1981.
Sports Illustrated reported that the letter to NBA executive vice-president and general counsel Rick Buchanan said Sterling would not pay the fine because it violated his right to due process. It also says the controversy "will be adjudicated," according to the report.
The person who spoke to the AP said that if Sterling doesn't pay the fine, the league could withhold $2.5 million from the Clippers when disbursing money to teams.
The league's Advisory/Finance Committee met via conference call as recently as Tuesday, according to league spokesman Mike Bass.
"The committee discussed the recent media appearances by Donald Sterling and Shelly Sterling, received updates on the hiring of Dick Parsons as the Los Angeles Clippers interim CEO and on his meeting yesterday with Clippers employees, and reviewed the status of the charge for termination of the Clippers' ownership," he said in a brief statement.
Bass added that the committee will reconvene next week.
The NBA's constitution, which Donald Sterling signed as controlling owner of the Clippers, gives its board of governors broad latitude in league decisions, including who owns the teams. Article 13 (d) of the constitution says that an owner cannot "fail or refuse to fulfil" contractual obligations to the NBA "in such a way to affect the Association or its members adversely."
Sterling has said he does not want to sell the Clippers. His estranged wife, Shelly, has said she'd like to keep her stake in the team even if her husband is ousted.
In a recent interview with CNN's Anderson Cooper, Sterling cast doubt on going to court if the NBA governors ultimately do vote to force him out.
"People want me to hire a wall of lawyers and them to have to hire a wall of lawyers and go to war," Sterling said on CNN. "I don't think that's the answer."
Sterling also said he was not a racist and apologized for the comments, which he made to a female companion. The recording of their conversation was posted to TMZ.com on April 25 and drew immediate condemnation.
Players threatened to boycott league games and several sponsors suspended their relationship with the Clippers. After Silver's quick rebuke in the days following the recording's release, many of the sponsors returned.
But the issue remains contentious. Star forward LeBron James said Monday that he understands it may take time, but he wants Sterling out of the NBA.
The Clippers were eliminated from the NBA playoffs Thursday night after a 104-98 loss to the Oklahoma City Thunder in the Western Conference semifinals.
AP Basketball Writer Brian Mahoney, AP Legal Affairs Writer Curt Anderson and Associated Press Writer Justin Pritchard in Los Angeles contributed to this report.