Moscow and Tokyo have been negotiating the Russian president’s visit to Japan since May.
"We are hoping that the visit will come into being," Koya Nishikawa told reporters following the negotiations in the Russian State Duma.
He added that the timeframe of the visit "is discussed by the Japanese government and the Russian Foreign Ministry in consideration of the situation in Russia-Japan relationship."
The lawmaker stressed that the ruling Liberal Democratic Party of Japan supported the idea of the visit and would assist with the organization of the visit.
Russia and Japan's relations have also been overshadowed by the Kuril Islands issue, which are controlled by Russia, but claimed by Japan.
In September, Putin and Japanese Prime Minister Shinzo Abe held bilateral talks on the sidelines of the UN General Assembly, agreeing to step up negotiations on a mutually acceptable solution to their countries' territorial dispute.