The ruling Liberal Democratic Party (LDP) proposed the date but opposition parties disagreed, citing ongoing discussions across parties, Kyodo reported. The committee will continue to discuss the schedule, it added, Reuters reported.
The LDP chose Sanae Takaichi as its new leader earlier this month after Prime Minister Shigeru Ishiba decided to resign both as LDP president and premier following a series of election losses.
But Takaichi's path to becoming Japan's first female prime minister has become murkier after the LDP's longstanding partner Komeito left the coalition last week, opening up the possibility of a premiership from an opposition party.
On Wednesday, the leaders of three major opposition forces - Constitutional Democratic Party (CDP), Democratic Party For the People (DPFP) and Japan Innovation Party - are due to meet for ongoing discussions on whether to band together to support a common candidate for the premiership.
The CDP, Japan's biggest opposition party, has suggested DPFP head Yuichiro Tamaki as a candidate to challenge Takaichi.
Takaichi is separately meeting one-on-one with the heads of CDP, DPFP and the Japan Innovation Party.
The LDP has lost its majority seat in lower and upper houses in elections since last year but remains the largest party in both chambers.