Japanese media on Wednesday said Abe, who took power almost exactly a year ago, made his intention known during a morning meeting with party leaders.
Hiroshi Suzuki, an Abe spokesman and the deputy cabinet secretary, said he was aware of the reports but was unable to give an immediate confirmation.
Taro Aso, the party's secretary-general, was quoted by NHK as saying that Abe, whose poll approval ratings has plumetted to 30 per cent, wanted to step down because he lacked the power to rally people together.
Abe's government has been plagued by scandals and gaffes despite naming a new cabinet line-up recently.
On Sunday, Abe, 52, said he "would not cling to my job as prime minister" if parliament failed to back a continuation of Japan's naval deployment in support of the US-led operations in Afghanistan.
His administration has suffered plummeting opinion poll ratings and a series of cabinet scandals and resignations, including one which ended in a suicide.
Abe is expected to hold a news conference later on Wednesday.