Among the other possibilities are ex-foreign minister Kishida and would-be first female PM Sanae Takaichi.
The premier has broken a century-old record for political longevity – but despite domestic comebacks and foreign policy wins, a succession of scandals and his mixed results with the economy will live long in the memory.
The ruling LDP-Komeito coalition maintains its strong lead over the lacklustre opposition parties, and is poised to retain the two-thirds supermajority it has enjoyed since 2016.
The 64-year-old will become Japan’s longest serving prime minister in November, having dominated the country’s politics since 2012.