Europe's No. 2 insurer hired Credit Suisse in September 2011 to explore its options for the unit, which has $28 billion (18 billion pounds) of assets under management.
AXA sought buyers for the business, which owns stakes in companies such as Europe's largest online travel agency Odigeo, ahead of new insurance regulations that require insurers to hold more capital.
The private equity unit is run by Dominique Senequier, one of France's best-known female executives, who may buy more than 35 percent of the business, with AXA retaining a 25 to 30 percent stake, the sources said.
The remaining stake would be held by other French investors.
One source said that while a deal was imminent, details had yet to be finalised.
Spokesmen for AXA in Paris and AXA Private equity declined to comment.
AXA shares fell 0.1 percent, slightly underperforming the European sector <.SXIP>, which closed 0.1 percent higher.
(Reporting By Anjuli Davies, additional reporting by Matthieu Protard, editing by Tommy Wilkes and Jane Merriman)