The reports quoted Griner as pleading guilty to the charges at Thursday's court hearing. They said that speaking through an interpreter, Griner said she had acted unintentionally because she was packing in haste.
Griner was detained in February at Moscow's Sheremetyevo Airport after vape canisters with cannabis oil allegedly were found in her luggage. She faces up to 10 years in prison if convicted of large-scale transportation of drugs.
The trial of the Phoenix Mercury star and two-time Olympic gold medalist began last week.
Griner returned to a Russian court Thursday to face her trial on drug charges as a senior Russian diplomat warned that US criticism of how Russia's handling the case wouldn't help her release prospects.
Griner's trial began last week amid a growing chorus of calls for Washington to do more to secure her freedom nearly five months after her arrest.
Before Thursday's hearing, Russian police escorted Griner, handcuffed and clad in a bright red T-shirt and sports trousers, into the courtroom past a crowd of journalists.
The athlete was detained in February at Moscow's Sheremetyevo Airport after vape canisters with cannabis oil allegedly were found in her luggage. She faces up to 10 years in prison if convicted of large-scale transportation of drugs.
Russian Deputy Foreign Minister Sergei Ryabkov warned on Thursday that “attempts by the American side to make noise in public ... don't help the practical settlement of issues”.
The White House said President Joe Biden called Griner's wife on Wednesday to assure her that he's doing all he can to obtain the athlete's release, as soon as possible.
They spoke after Biden read a letter from Griner in which she said she feared she'd never return home.
Washington hasn't made public its strategy in the case and the US may have little leverage with Moscow because of strong animosity due to Russia's military actions in Ukraine.
The State Department has designated Griner as wrongfully detained, moving her case under the supervision of its special presidential envoy for hostage affairs, effectively the government's chief hostage negotiator.
Asked about the possibility of Griner being swapped for a Russian jailed in the US, Ryabkov, the senior Russian diplomat, noted that until her trial is over “there are no formal or procedural reasons to talk about any further steps".
He warned that US criticism, including a description of Griner as wrongfully detained and dismissive comments about the Russian judicial system, “makes it difficult to engage in detailed discussion of any possible exchanges”.
“The persistence with which the US administration ... describes those who were handed prison sentences for serious criminal articles and those who are awaiting the end of investigation and court verdicts as wrongfully detained' reflects Washington's refusal to have a sober view of the outside world,” Ryabkov snapped.
The trial of the Phoenix Mercury star and two-time Olympic gold medalist was adjourned after its start last week because two scheduled witnesses did not appear.
Such delays are routine in Russian courts and her detention has been authorised through December 20, suggesting the proceedings could last months.
It was unclear if Griner would testify on Thursday.
Although Griner's supporters initially kept a low profile, calls for the US to take action spiked after the trial's first day.
The Rev. Al Sharpton, one of America's most prominent Black activists, this week called for Biden to arrange a prayer meeting with Griner, saying, "Four months is too long for this to have gone on, and I hope the President acts on her pleas to come home.”
An organisation called Win With Black Women sent Biden a letter saying Secretary of State Antony Blinken “has called Cherelle Griner, Brittney's wife, assuring her and stating publicly that Brittney's safe return was a matter of personal priority; however, we are concerned that the rhetoric does not appear to align with the actions taken to date. We urge you to make a deal to get Brittney back home swiftly.”
Russian news media have repeatedly speculated that Griner could be swapped for Russian arms trader Viktor Bout, nicknamed “the Merchant of Death”, who is serving a 25-year sentence in the US on conviction of conspiracy to kill US citizens and providing aid to a terrorist organisation.
Russia has agitated for Bout's release for years. But the wide discrepancy between Griner's alleged offense and Bout's global dealings in deadly weapons could make such a swap unpalatable to Washington.
Others have suggested that she could be traded along with Paul Whelan, a former Marine and security director serving a 16-year sentence in Russia on an espionage conviction that the US has repeatedly described as a setup.
Russia has shown no signs of backing off.
“This is a serious offense, confirmed by indisputable evidence ... Attempts to present the case as if the American was detained illegally do not hold up," Foreign Ministry spokesman Alexei Zaitsev said on Wednesday.
“The law has been violated, and arguments about the innocent nature of Griner's addiction, which, by the way, is punishable in some US states, are inappropriate in this case,” he said.