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NEW YORK — CKX, the company that now owns the rights to “American Idol” and the Elvis Presley brand, is in a little more conversation with at least one suitor.

The company stopped short of confirming a Wall Street Journal report that One Equity Partners — the private equity arm of JP Morgan Chase and Co. — was looking to acquire the company at $6 a share.

But CKX did announce, via statement on Monday, that “it is engaged in discussions regarding a possible transaction involving the sale of the company.” CKX said it released the statement “in response to market rumors.”

A CKX spokesman declined further comment.

CKX owns the rights to the “Idols” brand, including “American Idol,” through its 2005 acquisition of Simon Fuller’s 19 Entertainment. The company, run by Robert F.X. Sillerman, also owns the rights to the name, image and likeness of Muhammad Ali.

The $6 price tag means that CKX would be valued at about $558 million.

CKX’s stock rose 9 cents, or 1.5%, to $6.05 on the news.