Fighting for control of Aleppo has intensified in recent weeks and there have been some gains for rebel groups battling Syrian government forces.
Shoigu’s statements come as a surprise because Russia and the United States back different sides in the conflict while participating in talks to try to find a political solution.
“We are now in a very active phase of negotiations with our American colleagues,” the RIA news agency cited Shoigu as saying.
“We are moving step by step closer to a plan – and I’m only talking about Aleppo here – that would really allow us to start fighting together to bring peace so that people can return to their homes in this troubled land.”
Shoigu said about 700,000 people were still living in Aleppo and that those living in the eastern part of the city were “hostages of armed groups”.
Russia backs Assad in the five-year-old Syria conflict, while the United States wants to see Assad step down.
Earlier on Monday, Russian Foreign Minister Sergei Lavrov said Syrian militants had used a temporary ceasefire around Aleppo to regroup.
Deputy Foreign Minister Mikhail Bogdanov said Iran, Turkey and Saudi Arabia should play a more active role in helping to resolve the Syria crisis.
“(They should) sit down at the table and negotiate,” Bogdanov told the RIA news agency, saying he would meet representatives of the Syrian opposition in the Qatari capital, Doha, on Aug. 16.