Avon's German-traded shares advanced 6.2% from the Oct. 11 closing price in New York to $35.22 at 12:59pm in Frankfurt, Bloomberg News said.
L'Oreal may be lining up a cash bid of more than $44 a share for Avon, The Daily Mail said.
Avon's low debt levels make it an attractive target for potential buyers, UBS analysts said in a research note.
"We would not be surprised if L'Oreal scouted the acquisition trail," the analysts wrote.
Still, not everyone is convinced the deal makes sense. Chas Manso, an analyst at Evolution Securities in London, told Bloomberg News that an offer from L'Oreal is "a low probability event."