Brahimi, who saw Syrian President Bashar al-Assad on Monday and is planning to hold a series of meetings with Syrian officials and dissidents this week, is trying to broker a peaceful transfer of power.
More than 44,000 Syrians have been killed in a revolt against four decades of Assad family rule, a conflict that began with peaceful protests in March last year, but which has descended into civil war.
However, past peace efforts have floundered, with world powers divided over what has become an increasingly sectarian struggle between mostly Sunni Muslim rebels and Assad's security forces, drawn primarily from his Shi'ite-rooted Alawite minority.
Syrian Deputy Foreign Minister Faisal Makdad and an aide held talks at Russia's Foreign Ministry for less than two hours today, but declined to disclose any details of their visit.
Syrian and Lebanese sources said Makdad had been sent to Moscow to discuss the details of a peace plan proposed by Brahimi.
Foreign Ministry spokesman, Alexander Lukashevich, played down the idea that a specific plan was on the table in Moscow talks, at least none agreed by Moscow and Washington.
"We plan to discuss a range of issues linked to a political and diplomatic settlement in Syria, including Brahimi's efforts aimed at ending the violence and the launch of a comprehensive national dialogue," Lukashevich said.
Asked about rumours of a Russian-American plan to resolve the conflict, he said: "There has not been and is no such plan."
"In our talks with Mr. Brahimi and with our American colleagues, we are trying to feel a way out of this situation on the basis of our common plan of action that was agreed in Geneva in June."
World powers believe Russia, which has given Assad military and diplomatic aid to help him weather the uprising, has the ear of the Syrian government and must be a key player in peace talks.
Moscow has tried to distance itself from Assad in recent months and has said it is not propping him up, but Lukashevich reiterated its stance that Assad's exit from power could not be a precondition for negotiations.
Setting such a condition, he said, would violate the terms of an agreement reached by world powers in Geneva on June 30 that called for a transitional government in Syria.
"The biggest disagreement ... is that one side thinks Assad should leave at the start of the process - that is the US position, and the other thinks his departure should be a result of the process - that would be the Russian position," Dmitry Trenin, an analyst at the Moscow Carnegie Center said.
But Trenin said battlefield gains made by the Syrian rebels were narrowing the gap between Moscow and Washington.
On Saturday, Lavrov said Syria's civil war had reached a stalemate, saying international efforts to get Assad to quit would fail. Bogdanov had earlier acknowledged that Syrian rebels might win.,
Lavrov has said this month that Russia had no intention of offering Assad asylum and would not act as messenger for other nations seeking his exit. He has also said Russia lacks the sway to persuade him to step down.