The two leaders spoke by phone on Wednesday and agreed to move in that direction, the sources said on Friday.
When Abe and Putin last met in November in Beijing, they agreed to aim for Putin to visit Japan this year "at an appropriate time." An envisaged summit meeting of the two leaders in November is expected to lay the groundwork for Putin to visit Japan, observers said.
During their conversation Wednesday, Abe suggested they speak on the sidelines of summit meetings for the Group of 20 nations or the Asia-Pacific Economic Cooperation forum, both of which are scheduled for November.
Putin welcomed the prospect of meeting Abe then, the sources said.
The G-20 meeting is scheduled for Nov. 15 and 16 in Antalya, Turkey, while the APEC meet is planned for Nov. 18 and 19 in Manila. Should a meeting occur, it would be the leaders' first face-to-face talk in about a year.
During their Wednesday conversation, Abe raised concerns over a vote on a bill later that day by the upper house of the Russian Federal Assembly that would ban drift-net fishing for salmon and trout in Russia's exclusive economic zone.
Putin reportedly asked for Abe's understanding, saying the legislation was sponsored by lawmakers and aimed at protecting marine resources.
To work toward a visit by Putin this year, National Security Adviser Shotaro Yachi is expected to visit Russia as early as next month, the sources said. The government also intends to carefully explore the timing of a visit by Foreign Minister Fumio Kishida to Russia, which the Russian side considers a precondition for Putin's visit to Japan, sources said.