Court sources told CBS' Lee Frank a deal has reported been worked out to drop the case.
The alleged victim in the case has also reportedly agreed to the arrangement.
The prosecution will dismiss the high-profile case as early as Thursday, according to several media outlets all citing unidentified sources.
Prosecution spokeswoman Krista Flannigan declined comment, as did attorneys for the 20-year-old accuser. Defense attorneys did not return calls seeking comment.
District Attorney Mark Hurlbert was scheduled to hold a press conference Wednesday evening. Frank reports the fact that he plans to speak suggests the criminal case will be dismissed, as he would otherwise be violating a gag order.
The alleged victim's civil case seeking money from Bryant is also expected to be dropped, reports Frank.
Bryant, 26, has said he had consensual sex with a then-19-year-old employee of a Vail-area resort where he stayed last summer. If convicted, the Los Angeles Lakers star would face four years to life in prison or 20 years to life on probation, and a fine up to $750,000.
L. Lin Wood, an attorney handling the woman's federal civil lawsuit against Bryant, said that case was intact.
"There has been no settlement of the civil lawsuit and there have been no discussions concerning a settlement," he said as he stood in the hallway of the Eagle County courthouse. He declined comment when asked about the criminal case.
The reports surfaced as jury selection began to wrap up. Attorneys and District Judge Terry Ruckriegle had hoped to seat a 12-member jury this week, with opening statements coming next Tuesday.
Defense attorneys this week asked the judge to dismiss the assault charge, saying prosecutors had refused to turn over details that could suggest he is innocent. Court rules require prosecutors and defense attorneys to exchange evidence and witness opinions before trial, a process called discovery.
In a motion made public Wednesday, defense attorneys said a forensics expert whom prosecutors had planned to call as a witness had information that "undermined the accuser's allegations and the prosecution's case, and corroborated Mr. Bryant's defense on a central issue — the cause and significance of the accuser's alleged injuries."
The filing said those opinions were not disclosed to the defense until they contacted the expert Friday, despite repeated requests to prosecutors for the information. Prosecutors have said they have turned over all information they were required to.
"A person's life and liberty are at stake," the defense attorneys wrote. "The game of hide-the-ball, find-it-if-you-can discovery is intolerable. This court must vindicate Mr. Bryant's constitutional rights and impose meaningful sanctions against the prosecution."
The defense has also argued that injuries found on the woman could have been caused by sex with someone else in the time surrounding her encounter with Bryant, including someone afterward and before she went to a hospital. The woman's attorneys have denied that claim.
Defense attorneys asked the judge to either dismiss the case or bar prosecutors from introducing any expert testimony relating to the accuser's injuries. The judge gave prosecutors until Tuesday to respond.
The motion does not identify the expert, but prosecutors this spring said they planned to call former New York City medical examiner Michael Baden to testify about the woman's injuries.
Hurlbert said during a July 19 hearing he had decided against using Baden. He did not elaborate.
The motion was first reported by ABC News, which cited unidentified sources who said Baden told prosecutors the woman's injuries could have been caused by consensual sex. Baden did not return messages Wednesday.