The New York Times has theorised that Peltz may be keen to break up P&G based on his previous (but unsuccessful) attempts to do so with PepsiCo. The paper also reported that analysts from Bernstein have already sent letters to David Taylor, chief executive of P&G, supporting the idea.
In a public statement, P&G said it "welcomed all investment" in the company but declined to comment further.
P&G has been under shareholder pressure to improve its top line, reported the FT. It has already reduced its marketing and other costs by $7bn, and Taylor has promised to cut a further $10bn.
The group has also been streamlining its stable of brands, selling 40 off to Coty in 2015.