His five-year contract will expire early next year; rival Warner Music Group has quietly alerted Cohen that a top post is available, senior AOL Time Warner execs told NEWSWEEK. Formal talks haven’t started–Cohen’s current employer, Vivendi Universal, has rights to try to re-sign him, and rivals risk being sued if they interfere. Cohen won’t comment, and Warner Music boss Roger Ames will only say he’s a longtime Cohen fan.

Cohen has hit mostly high notes at the Universal Music Group label. Def Jam rap stars, such as Ja Rule and Jay-Z, and new artist Ashanti, have helped Universal dominate the charts. The hip-hop exec has scored in rock music, too, with an established group like Bon Jovi and the new act Sum 41. The label is launching a clothing line–Def Jam University–and TV and concert businesses.

Though Warner Music execs are all for courting Cohen, some of the bosses at their parent, AOL Time Warner, are concerned about Cohen’s hardball reputation. In May a jury ordered Island/Def Jam and Cohen to pay $132 million in damages to another record label because of alleged strong-arm business practices. Cohen’s colleagues expect the court will ultimately overturn the damages. They also blame his corporate bosses at Vivendi Universal for the outcome, saying that attempts to settle the case out of court for $3 million to $5 million were vetoed by higher-ups. In upcoming job talks, it appears Cohen will be the one with veto power.