Foreign ministry spokeswoman Maria Zakharova indicated that talks on prisoner exchanges had been going on for some time but without producing a result.
Kremlin spokesman Dmitry Peskov told reporters that "so far there are no agreements in this area".
They were responding to comments by U.S. Secretary of State Antony Blinken that Washington had made Moscow a "serious offer" to secure the release of Griner and former U.S. marine Paul Whelan, also detained in Russia.
"The issue of the mutual exchange of Russian and American citizens in detention on the territory of the two countries was at one time discussed by the presidents of Russia and the United States," Zakharova said, apparently referring to conversations pre-dating Russia's Feb. 24 invasion of Ukraine.
"They gave instructions to the relevant authorized structures to carry out negotiations. These are being conducted by the competent departments. A concrete result has not yet been achieved."
Negotiations would need to take into account the interests of both sides, she said.
Blinken said on Wednesday he would discuss the Griner and Whelan cases with his Russian counterpart in the coming days.
"When discussing such topics, you don't conduct information attacks," Peskov said in an comment that appeared to reflect irritation with Washington's very public diplomacy on the issue.
On Wednesday, a source familiar with the situation confirmed a CNN report that Washington was willing to exchange Russian dealer Bout, who is serving a 25 year-prison sentence in the United States, as part of a deal.
A Russian lawyer for Whelan has previously said he believed Moscow wanted Bout to be part of a swap for Whelan.
Griner, detained at Moscow's Sheremetyevo airport in February with vape cartridges containing cannabis oil in her luggage, was in the courtroom on Wednesday in the latest hearing of her trial on drug charges. The next hearing is set for Aug. 2.
"From a legal point of view, an exchange is only possible after a court verdict," Griner's lawyer in Russia, Maria Blagovolina, said in a statement.
Whelan was sentenced in 2020 to 16 years in prison in Russia, accused of spying. He denied spying and said he was set up in a sting operation.
