Finance Minister Sadakazu Tanigaki has said that, as prime minister, he would not visit a controversial Tokyo war shrine that has angered neighboring Asia countries.
Koizumi's visits to the Yasukuni shrine have spiked tensions with China and South Korea.
Speaking to reporters after a meeting with Koizumi, Tanigaki said he told the premier he will formally announce his plan to campaign for the post Thursday afternoon.
Koizumi's term as president of the ruling Liberal Democratic Party ends Sept. 30, and he has said he won't run again. Whoever wins the party election is almost certain to be named prime minister by Parliament's LDP-dominated lower house.
Tanigaki's announcement would make him the first formal candidate in the race.
He has vowed that, if he becomes prime minister, he would work to improve both Japan's financial health and its relations with China and South Korea, Kyodo News agency said.
In particular, he has indicated he would not visit the controversial Yasukuni war shrine, which critics at home and abroad say glorifies Japanese militarism.
Koizumi, whose annual visits to the shrine have helped sour ties with Beijing and Seoul, told him to handle the issue "boldly," Tanigaki said.
Abe, who is the government's top spokesman, is known for promoting a more assertive Japan in dealing with China and North Korea