It said the possible order for the planes would likely be placed via Rostekhnologii, or Russian Technologies, a corporation which groups most of the state-owned defence enterprises.
Aeroflot was not immediately reachable for comment on the report.
Aeroflot, which historically has bought the bulk of its fleet from Airbus, has favoured arch rival Boeing more recently as its preferred supplier.
The company, which was set up in 1923 as the Soviet national airline, embarked on a campaign to renew its fleet last year after the state merged fragmented aviation assets into its flagship carrier.