Beauty product company Coty Inc, whose $10 billion bid for larger rival Avon Products Inc was rejected earlier this month, said it might raise its offer if it was invited to examine the direct seller's books.

Coty said it remained interested in discussing its proposal with Avon, which named Johnson & Johnson senior executive Sherilyn McCoy as its new CEO last week.

At this stage, without being invited to complete due diligence, we have no way of knowing the best price we can ultimately pay to Avon shareholders, the company said in a statement.

Coty had made an unsolicited $23.25 per-share offer for Avon, which is seeing declining sales at home and in key markets including Brazil and Russia and also facing a U.S. probe into overseas bribery allegations.

Avon rejected the bid, arguing that the company's value could rise more under a new CEO than as part of Coty.

Coty said it was confident in its ability to finance the acquisition and that it has arranged for equity commitments of more than $5 billion. It added that it has also received a highly confident letter from J.P. Morgan Securities LLC for debt financing.

Avon's former shareholder Richmont Holdings said last week that it was preparing a takeover offer for the beauty products company, according to Fortune magazine.

Richmont Chairman John Rochon had unsuccessfully tried to buy Avon in the late 1980s when he was the chief executive at privately held rival Mary Kay, Fortune said.

Avon shares closed at $23.52 on Friday on the New York Stock Exchange. They were trading up nearly 1 percent before the bell.

(Reporting by Juhi Arora in Bangalore; Editing by Viraj Nair)