(UPDATE) It looks almost official. TV Tokyo reports (1/9/2014) that Hosokawa has decided to run, and Koizumi has already pledged support. TV Tokyo says "Hosokawa and Koizumi are both popular with voters", which is probably true.
Now it gets somewhat interesting, with two weeks left till the official announcement of candidacy.
Former prime ministers - Morihiro Hosokawa (Japan New Party, 1995-1996) and Junichiro Koizumi (LDP, 2001-2006) may join forces, with Mr. Hosokawa running in the gubernatorial election for Tokyo set to be held on February 9, according to the latest Asahi Shinbun article.
Mr. Hosokawa was the first prime minister since 1955 who was not from Liberal Democratic Party. His coalition later evolved into Democratic Party of Japan. He has taken to pottery after he retired from politics.
Mr. Koizumi retains substantial influence within/out LDP even after he retired from politics, and he has caused a stir among anti-nuclear citizens who look at Koizumi's anti-nuclear stance with great suspicion. Koizumi doesn't seem to care about his critics, though, and continues to openly speak up against nuclear energy.
Hosokawa's potential entry into the gubernatorial race, from Asahi Shinbun (1/9/2014; part):
Two weeks till the official announcement on January 23 of the Tokyo gubernatorial election, the name of the former prime minister Morihiro Hosokawa has suddenly surfaced as a candidate. As Yoichi Masuzoe, former Minister of Health and Labor, has announced his intention to run with the LDP support, Hosokawa's entry into the race could vastly change the election landscape.
Mr. Masuzoe is considered to be one of the favorite to win the race. But if the alliance of Mr. Hosokawa and the former prime minister Junichiro Koizumi materializes under the "anti [beyond] - nuclear" slogan, it could become the eye of a storm.
It's been 15 years since Mr. Hosokawa retired from politics. The main reason he is considering a comeback is his sense of crisis over nuclear power plants and energy issues.
According to a person involved in Japan New Party, which Mr. Hosokawa started [it doesn't exist any more], Mr. Hosokawa told him in early January that "The energy policy of the Abe administration may harm the nation. It is important to appeal anti (beyond) - nuclear to the voters in the Tokyo gubernatorial election. It's not the matter of win or lose."
This person says the preparation is already underway should Hosokawa decide to run. "Depending on his decision, anything is possible. It's been all prepared."
The key to Hosokawa's candidacy is Mr. Koizumi's intention.
The two met and spoke last fall, and promised to join forces in anti-nuclear movement. The person involved [in Japan New Party] is hopeful, saying "If Mr. Hosokawa runs, Mr. Koizumi will definitely support him. If Mr. Hosokawa joins forces with Mr. Koizumi, the election landscape will suddenly changes." He says Mr. Hosokawa is watching Mr. Koizumi carefully.
... On the other hand, LDP, who will support Mr. Masuzoe, is openly wary. The party has already started gathering information on Mr. Hosokawa's moves. One of the senior party members says, "We're not afraid of Mr. Hosokawa, if he is alone. However, if Mr. Koizumi is behind him, it could lead to a nuclear fusion [meaning "very significant event that could jeopardize their soon-to-be-declared candidate Masuzoe"]."
If it is going to be a choice among Mr. Kenji Utsunomiya (attorney backed by Social Democrats and Communist Party), Mr. Yoichi Masuzoe (scholar-author-TV personality-politician backed by LDP and DPJ) and Mr. Hosokawa (with Mr. Koizumi's backing) and if I am forced to choose, I'll be totally at a loss for whom to vote. Mr. Utsunomiya and his message look too "1990s", Mr. Masuzoe is too slick and sleazy for my liking. Beyond the historical significance, Hosokawa was utterly ineffective as the prime minister who effectively threw out the job in only 9 months.
Hosokawa's ancestor was the lord that governed today's Kumamoto after Kiyomasa Kato, extremely popular lord who was displaced by the Tokugawa administration in the 17th century. Maybe Hosokawa is more fit for governing a prefecture, instead of the entire nation.
Asahi's hope that the anti-nuclear stance will get many votes seems little more than a hope, though. From all indications, the Fukushima nuclear accident is long over in the minds of most Japanese.
If Hosokawa runs in the race, it will be the very first time that a former prime minister of Japan runs for a prefectural office. At least I've never heard of it.