Cerberus, a New York-based private equity firm, would also take an equity stake in Avon, which has a market capitalization of close to $1.6 billion and long-term debt of around $2.2 billion, the people said. Avon also had $587 million in cash as of the end of September.

Separately, activist investor Barington Capital Group has built up a 2.8 percent stake in Avon and is launching a campaign to force changes at the company, the people said. Barington would oppose a deal with Cerberus that would value Avon near its current valuation, one of the people added.

The sources asked not to be identified because the matter is confidential. Avon, Cerberus and Barington declined to comment.

Avon shares ended trading in New York up 7 percent at $3.99 after the Wall Street Journal first reported on the news.

Founded in 1886 by a traveling book salesman, and known for its door-to-door sales, the company has been losing its representatives known as "Avon Ladies" amid weak demand in the United States and Brazil.