Avon, whose brands include Skin-So-Soft, Anew and mark, said Thursday that Coty told it in a letter that it was raising its offer to $24.75 per share from $23.25 per share.
Coty's financing sources include Berkshire Hathaway Inc. along with Joh. A. Benckiser GmbH, the German holding company that controls Coty, and BOT Capital Partners. JPMorgan Securities would provide debt financing.
The revised bid is a 15 per cent premium to Avon's Wednesday closing price of $21.60. Avon shares fell 71 cents, or 3.3 per cent, to close at $20.89 Thursday.
Avon had rejected Coty's $10 billion offer last month, but Coty has remained interested. It said in the letter to Avon that it wants to look at Avon's books to confirm estimates and learn more about Avon's ongoing bribery investigation and litigation.
Coty says it will withdraw its latest bid if it doesn't receive a response by the close of business Monday.
Coty's letter indicated Avon has said it is not interested in reviewing any proposal until after newly installed CEO Sherilyn McCoy has completed a review of all of Avon's business operations.
On Thursday, Avon said its board will consider Coty's letter in due course.
Founded in 1886, Avon became a fixture in households across the country as its legions of "Avon ladies" went door to door selling makeup to family, friends and acquaintances.
Now, Avon is in transition. McCoy, a long-time Johnson & Johnson executive, has been in place less than a month. She replaced CEO Andrea Jung, who had come under fire for failing to stem the company's declines and wrap up the bribery investigation, which started in China in 2008 and has spread to other countries.
The company's profit has shrunk over the past three years. It has frequently missed analysts' earnings expectations and posted weak sales in some of its largest markets, including Brazil and Russia. Avon said last week that its first-quarter net income fell 82 per cent, hurt by a bigger restructuring charge and higher commodity and labour costs.
One analyst said the move makes it more likely a deal will result.
"We believe the revised offer is a fair starting point to negotiations and increases the likelihood Avon is acquired," said Stifel Nicolaus analyst Mark Astrachan. "Absent an agreement, Avon's board must present a compelling argument to shareholders why the company should remain independent, particularly given numerous fundamental and operational problems and highlighted by disappointing first quarter results, in our view."
Rumours of other possible bids for the New York company have been swirling. A media report last week said private equity firm Richmont Holdings is structuring an offer for Avon, but so far nothing has materialized.
Meanwhile, credit ratings agency Fitch Ratings put Avon on rating watch negative. Fitch said in a statement that if the deal goes through and is financed with significant amounts of debt the combined company's credit protection measures would not be in Avon's current rating category. Avon's senior unsecured debt is currently rated "BBB-," the lowest investment-grade rating.