They are, not surprisingly, all men, with the first being Deputy Prime Minister Taro Aso.
Aso, 79, who also serves as finance minister, is expected to succeed Abe as interim premier.
The gaffe-prone Aso, who is known as a manga buff, acts as interim prime minister and that could galvanise the opposition camp.
In 2009, when Aso was prime minister, sinking popularity for his Cabinet helped the main opposition Democratic Party to oust his ruling Liberal Democratic Party (LDP).
The victory ended more than a half-century of almost unbroken rule by the LDP.
Another possible successor is Chief Cabinet Secretary Yoshihide Suga.
Since Abe was inaugurated in December 2012, Suga has been the country’s government spokesperson, officially known as the chief cabinet secretary.
Only Aso and Suga, 71, have retained their respective positions since the start of Abe’s Cabinet.
Defence Minister Taro Kono, 57, is another possible successor.
Kono had served as foreign minister for a little more than one year, before taking the current post.
Unlike many Japanese politicians, Kono, a graduate of the School of Foreign Service, Georgetown University in the U.S., is an outspoken lawmaker who has opposed nuclear power generation.
His father Yohei Kono was a long-time speaker of the House of Representatives.
Then there is former defence minister Shigeru Ishiba, 63, who the Japanese media have for long named as a possible successor to Abe.
Ishiba, a railroad enthusiast, took the party’s leading posts such as secretary general and chairman of the party’s policy research council.
Last but not least of possible successors to the ailing Abe is former foreign minister Fumio Kishida
Kishida served as foreign minister for more than four and a half years and he leads one of the LDP’s biggest factions.
The 63-year-old chairs the party’s policy research council.
He remains a surprisingly obscure figure. (DPA/NAN)