"It is possible it will be timed to seek voter response (to the change) when a new Cabinet is launched and support for it is likely to be high," Shunichi Suzuki, head of the LDP's General Council, told a TV program. "I'm one of those who are tempted by that idea."
The LDP is to hold its presidential election on Sept. 14 to pick Abe's successor who will then be chosen as the country's prime minister at an extraordinary Diet session on Sept. 16, given the party's dominance in the House of Representatives.
The new premier is expected to form his Cabinet the same day.
Yoshihide Suga, who has been chief Cabinet secretary and Abe's right-hand man for nearly eight years, is on course to secure about 70 percent of the vote among party lawmakers, making him the clear front-runner.
Abe said late last month he will step down due to ill health.
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