"We hope for a quick and positive response from Brussels," Lavrov said after talks with Polish counterpart Radoslaw Sikorski.
"The Polish side has confirmed that it will support this draft (agreement)," the Russian International News Agency Novosti quoted Lavrov as saying.
United Press International was unable to find Polish confirmation of the report, but also saw no Polish dispute of it.
Having visa-free travel with the EU has become a major foreign-policy goal in Moscow's relations with Brussels, the Russian news agency said.
Lavrov said Wednesday the mutual scrapping of visa requirements between Russia and the EU would have a "transformative" effect on the entire European and Euro-Atlantic political relationship.
Most European countries support visa-free travel for Russians, while several EU states reject it for political reasons, Russian Prime Minister Vladimir Putin said Wednesday.
Germany and France are among the supporters, the official Voice of Russia's international radio broadcasting service said.
Italian Prime Minister Silvio Berlusconi told Russian President Dmitry Medvedev in July the resistance to visa-free travel came largely from Eastern European countries.
Celebrity Families of 2014 [PHOTOS]