But Yoichi Masuzoem the health minister, said all cabinet members, including Kaoru Yosano, the finance minister who some had earlier speculated might refuse, backed the election plan on Tuesday.
Aso, who is scheduled to give a news conference later on Tuesday, faces an uphill task in trying to keep his job and his party in power.
The premier survived a no-confidence motion in parliament last week due to the LDP's dominance in the current house, but the latest newspaper polls indicate that dominance is about to end.
A poll published in the Mainichi newspaper puts the main opposition Democratic Party of Japan (DPJ) ahead of the LDP by a two-to-one margin.
Fifty-six per cent of voters indicate they would choose the DPJ and 23 per cent say they would vote LDP, according to the poll.
Another poll by Asahi newspaper showed similar results, with 49 per cent of respondents supporting the Democrats, and only 22 per cent behind Aso's party.
A victory by the Democrats would end more than 50 years of almost unbroken rule by the LDP.