The study involved 10,090 people. When asked whom they would prefer if they were to vote, 45% preferred Kono.
Former Foreign Minister Fumio Kishida, who is believed to be one of the favourites in the race, and former Minister of National Affairs Sanae Takaichi received 18% each. They are followed by LDP Deputy Secretary-General Seiko Noda, who has 7% support.
The party leadership election is scheduled for 29 September. It comes after Prime Minister Yoshihide Suga announced his decision to step down amid plummeting popularity over his handling of the coronavirus response, including the slow rollout of vaccines.
The four-way contest is set to become the first party leadership race with two female candidates on the ballot in a country where women are vastly underrepresented in politics.