Russian and U.S. diplomats held two trilateral meetings last month with Brahimi, who is trying to find a diplomatic solution to end the nearly 22-month-old conflict between Syrian President Bashar al-Assad's government and its opponents.
Russia and the United States both support Brahimi's efforts to forge a peace deal based on an agreement reached by world powers in Geneva in June, which called for the creation of a transitional governing body, but they are at odds over Assad.
Russia says Assad's exit from power must not be a precondition for a political solution in Syria, where more than 60,000 have been killed since the conflict began with a government crackdown on protests in March 2011.
"A trilateral meeting with participation of Mikhail Bogdanov, (U.S. Deputy Secretary of State) William Burns and Lakhdar Brahimi is planned for January 11 in Geneva," Interfax quoted Bogdanov as saying.
Bogdanov, the Kremlin special envoy for Middle East affairs, met Burns and Brahimi in Geneva on December 9, three days after Brahimi met Russian Foreign Minister Sergei Lavrov and U.S. Secretary of State Hillary Clinton in Dublin.