The Hollywood Reporter, citing All Things Digital, says Parker has joined a group led by investors Ron Burkle and Doug Teitelbaum that is vying for the company. The asking price is $2.5 billion.
Parker is a billionaire thanks to his stake in Facebook. He was portrayed by Justin Timberlake in "The Social Network."
He is now advising Spotify, a music streaming service based in Sweden that has not launched in the United States and is at odds with WMG and Universal Music Group.
Metallica, a WMG act, sued Napster in 2000 after an unreleased song spread on the peer-to-peer network. Napster lost the case and was closed down.
ATD says Burkle and Teitelbaum lead one of at least five bidders looking at Warner, and a decision could come within weeks.
Pistorius testifies he didn't consciously pull trigger when he shot girlfriend
Pot vending machine to debut