The election, which will also determine the new prime minister, is to take place on 29 September.
The poll also showed that 26.6% would vote for former Defense Minister Shigeru Ishiba, and 18.8% chose former Foreign Minister Fumio Kishida.
More than a half of the population supported the intention of incumbent Prime Minister Yoshihide Suga to step down over the fall of his approval ratings caused by his response to the COVID-19 challenges.
The survey was conducted from September 4-5 by randomly dialing 1,071 eligible voters.
Only Kishida has officially announced his campaign bid so far.
Taro Kono used to serve as Japan's defence and foreign minister, and now he is in charge of the COVID-19 vaccination drive and administrative and regulatory reforms.