CORRECTED-CBOE would consider going private if benefits shareholders -COO

(Corrects paragraph one to delete "group" from company name)

By Ann Saphir

Feb 14 (Reuters) - CBOE Holdings Inc, which became a publicly held company in 2010 after years of effort, would consider going private again if doing so would benefit its shareholders, a top executive suggested on Thursday.

Private equity firm Carlyle Group recently approached Nasdaq OMX Group Inc about taking the exchange operator private, but the talks fell apart over a disagreement on price, sources familiar with the deal said on Monday.

While CBOE is in a "terrific spot" as a public company currently, CBOE Chief Operating Officer Edward Tilly said at a Credit Suisse financial services forum, "If valuations as a result of conversations with Carlyle lifts all boats, so be it ... We would have to entertain changes in our structure."

Tilly has been picked to succeed Bill Brodsky as chief executive of CBOE in May.

(Reporting by Ann Saphir; Editing by Gerald E. McCormick)