Shares of Avon closed nearly 7 percent higher on the day.
Avon and Cerberus aim to reach a deal this month, according to the wire service. Cerberus would become the company's biggest shareholder and would make a minority investment, the report said.
Cerberus did not immediately respond to CNBC's request for comment. The report comes amid struggles for Avon. Its shares have fallen nearly 60 percent this year.
An activist group including Barington Capital has built a more than 3 percent stake in Avon, and would oppose a private equity deal, Barington said. It wants the company to reduce costs and appoint new independent directors as part of a broader restructuring plan.
In a statement, Avon did not address the Cerberus report, but said it was aware of Barington's views and "welcomes open communications with and feedback from our shareholders."
Rumors have swirled around Avon this year. Its shares whipsawed Wednesday amid rumors that Oprah Winfrey invested in the company. A spokesperson for the entertainment mogul denied the reports.
Avon shares also spiked in May after a hoax takeover bid.