The offer is believed to be for about $600 million, according to the Hollywood Reporter.
In addition to "Idol," CKX owns the rights to the names, images and likenesses of
The CKX board of directors is evaluating the proposal, "as well as other potential strategic alternatives," it said in a statement, has retained Gleacher & Company as its financial adviser and Wachtell, Lipton, Rosen & Katz as legal adviser.
CKX also said, "There can be no assurance that it will enter into any agreement with respect to any transaction, or as to the timing or terms thereof, including price."
Fuller left 19 Entertainment, of which he was CEO and founder, in January.
Fuller and partner Roger Jenkins, formerly of Barclays Capital, have amassed a $1 billion acquisitions fund, according to ABC News.
One Equity Partners, a private equity arm of JPMorgan Chase, also is eyeing CKX as a takeover target.