Barely a month after reports surfaced that Jay-Z would be starting his own record label with computer giant Apple, word is swirling around again that the former Def Jam President is still adamant about owning a label and has been in talks with Warner Music Group honcho Lyor Cohen.

Jay-Z stepped down from his President/CEO position at Def Jam Records in December 2007 after a four year run.  He is still tied to Def Jam as an artist and owes the label one more album which will cut his contractual obligation with the hip hop powerhouse.

The New York Daily News reports that an industry insider revealed to them that the label Jay-Z wants to launch with is called the Carter Music Group but Cohen, who signed Jay to Def Jam during his tenure as a CEO at the label, says he has not talked to the rapper about launching a label but would jump at the opportunity.

“I would be honored and privileged to work with him again,” Cohen said.  “Bringing Jay-Z to the Warner Music Group would be a privilege and a coup.  I'd do it in a heartbeat.”