Fukuda, 71, served as chief cabinet secretary under Prime Minister Junichiro Koizumi. He is the son of former Prime Minister Takeo Fukuda.
Taro Aso, the party’s secretary-general, is also expected to run for leader of the LDP. The two men were expected to register as candidates Saturday morning.
The party’s 387 parliamentary members and 141 prefectural representatives will vote Sept. 23.
Fukuda is a contrast to Abe in many ways, starting with his age. Abe was the youngest Japanese prime minister in decades. They also disagreed on foreign policy, with Fukuda more conciliatory to China and other nearby rivals.
Aso more closely resembles Abe, the newspaper said.