That would give Abe, whose resignation in 2007 after an earlier stint started a spate of revolving-door premiers, a chance to achieve his goal of revising the U.S.-drafted, post-war constitution, which has never once been amended.
Revising the constitution's pacifist Article 9 to loosen limits on the military remains a divisive issue domestically, but China's rising regional influence has given conservatives in favour of the change fresh ammunition.
"Constitutional revision will be a major theme," former education minister Hakubun Shimomura, a close Abe ally, told Reuters in an interview, referring to a possible third term.
Abe would also focus on reviving an economy faced with deep-rooted problems of an ageing, shrinking population, he said.
The LDP is set on Sunday to formalise a rule change to allow party presidents a third consecutive three-year term, clearing the way for Abe to run again after his current tenure as party chief ends in September 2018. If the LDP stays in power, that would make it highly likely Abe remains premier.
But Japan must hold its next general election by late 2018 and an upper house poll must be held the following year. So even after the LDP changes its rules, nothing was for sure, Shimomura said.
"Just because he can extend his term as LDP president doesn't automatically mean he can extend his stay as prime minister," he said.
Japan has avoided the sort of populist surge that helped Donald Trump win the U.S. presidency, and is boosting right-wing parties in Europe.
That is partly because Abe's return to office in 2012 has given his ultra-conservative backers a voice in the corridors of power.
Popularity ratings at a robust 60 percent, buoyed by a chummy summit with Trump last month, a lack of viable rivals in his party and single-digit support for the main opposition Democratic Party, would appear to mean Abe is well-placed for a third LDP presidential term.
"It's never over 'til the fat lady sings, but it's his for the taking," said Jeffrey Kingston, director of Asian studies at Temple University's Japan Campus.
"He wants to be there for the Olympics," he said, referring to the 2020 summer games in Tokyo.
'SCHOOL FOR SCANDAL'
Recent questions in parliament about a sweetheart land deal benefiting a private school with a nationalist agenda and links to Abe's wife have, however, been a reminder that Abe may be vulnerable, although he has denied any wrongdoing.
"Abe has been considered as the most stable government among major countries. So this is really worrying," said a senior currency trader, who declined to be identified.
Political analysts are betting for now that Abe can ride out the storm over the purchase of state-owned land by educational institution Moritomo Gakuen at rock-bottom prices.
Foremost among factors contributing to his durability is the opposition Democratic Party's inability to erase memories of its fractious three years in power.
Abe says he has overcome a chronic intestinal ailment that contributed to his 2007 resignation, but speculation about his health pops up from time to time.
The outlook for the world's third-biggest economy also remains uncertain despite four years of his "Abenomics" recipe of hyper-easy monetary policy and fiscal spending.
The LDP could also face a challenge if popular Tokyo Governor Yuriko Koike, a former defence minister in Abe's first cabinet, can win national support for her new local party.
The LDP has won two general elections and two upper house polls by landslides under Abe, but has still not regained the number of votes obtained in the 2009 poll when it lost power, due to record low turnout as voters fed up with their choices stayed at home.
That means the LDP and its junior partner could lose their two-thirds "super majority" in the lower house if a fragmented opposition unites, although losing their simple majority is less likely, analysts say.
"The policies Abe is pushing don't necessarily face smooth sailing," said political analyst Harumi Arima, referring to the constitutional revision and restarting nuclear reactors offline since the 2011 Fukushima atomic disaster.
"That means he could be overturned in the next election."
(Reporting by Linda Sieg; Editing by Linda Sieg)
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)