Shares were up 9.6% to $3.51 a share.
The London-based company said in a statement that "there can be no assurance any transaction will result from these discussions." Avon also said it "does not intend to make any additional comments regarding these discussions unless and until it is appropriate to do so, or a formal agreement has been reached."
The Wall Street Journal reported earlier that Avon was nearing a sale to Natura Cosmeticos and that the deal could be announced Wednesday.
Avon has been struggling in recent years. In January, the company cut 2,300 jobs.