Avon 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. The revised bid is a 15 percent premium to Avon's Wednesday closing price of $21.60.
Avon had rejected Coty's $10 billion offer last month, but Coty has remained interested. Coty says it will withdraw its latest bid if it doesn't receive a response by the close of business Monday.
Avon says its board will consider Coty's letter in due course.
Its stock jumped $1.61, or 7.5 percent, to $23.21 in premarket trading.
