Abe is now looking at the option of the transfer of just two islands – Habomai and Shikotan – to end the decades-long standoff, according to several government sources who spoke with Kyodo.
The news agency added that government officials regarded the handover of two other islands – Iturup and Kunashir – as "unrealistic."
This comes days before the Japanese prime minister is expected to come to Moscow for talks with Russian President Vladimir Putin. The peace deal is expected to be high on their agenda.
The row over four Southern Kuril islands stopped the Soviet Union from signing the post-WWII deal with Japan, which sees them as its occupied northern territory.