"In the past several days an intensive document exchange on the situation in Aleppo has taken place," Ryabkov said.
"We are close to reaching an understanding, but I want to warn against high expectations," Ryabkov added, Reuters reported.
The Kremlin said on Wednesday that a potential US-Russia deal to allow Syrian opposition to safely leave Aleppo was still on the agenda.
Russian Foreign Minister Sergei Lavrov was due to meet US Secretary of State John Kerry in Hamburg later on Thursday after the two men held talks on Wednesday.