Abe floated the idea of holding a vote on October 22 or October 29 in meetings with senior ruling party officials, Jiji Press and the Asahi Shimbun reported, citing unnamed government and ruling party sources.
Other media reported similar stories but with a wider range of options for the timing of the snap election, including in December.
The reports come as Abe has seen a recovery in public support after the figures plummeted in the past few months over an array of political troubles, including allegations of favouritism to a friend in a business deal that Abe strongly denies.
Public support for Abe had fallen to the lowest level of his premiership in July, but since has recovered gradually as Pyongyang raised global tensions with repeated missile and nuclear tests including missile launches over Japan.
His popularity is now hovering around 40 percent.
Experts say his resurgent popularity is thanks more to a weak and fragmented opposition than support for his policies.
Abe has called for a boost to the country's defences and worked to strengthen the key security alliance with the US and defence cooperation with other like-minded countries.
He has pushed a nationalist agenda since coming to office in December 2012, alongside a massive policy effort to end years of on-off deflation and rejuvenate the world's third- largest economy.
"All the lower house members are beginning to think that (general elections) would come in the not too distant future," the ruling Liberal Democratic Party (LDP)'s senior official Wataru Takeshita said Saturday in a speech in western Japanese city of Tokushima.
Some lawmakers, including ruling party members, however, have warned about a potential political paralysis during the election campaign period amid lingering worries over North Korea.
LDP officials were not immediately available to confirm the reports on Sunday.