"Step by step we are getting closer to the situation in which -- and I'm only speaking about Aleppo here -- we will be able to begin battling together so that there is peace on this territory," Shoigu told Rossiya 24 television.
In the interview conducted on Saturday but shown only today, Shoigu said Moscow is in close negotiations regarding the city, where Russian planes and regime forces are battling rebels for control.
Shoigu said Moscow and Washington are still deeply at odds over the situation in Aleppo, accusing rebels of holding civilians hostage and waging brutal suicide bombings.
He blasted accusations that Moscow has imposed a blockade on rebel-held areas, calling them "untrue" and "propaganda".
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He said suicide attacks by rebels have included loading an armoured vehicle with explosives and welding it shut.
"That's moderate opposition? Who is this?" he said.
"There are many issues there that we are yet to decide on with our American colleagues," he said of Aleppo. "We are now in a very active stage of negotiations with American colleagues.