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Nasdaq has taken a huge hit to its tech-savvy image due to its botched handling of the biggest IPO last year, Facebook, and last month's trading shutdown.

Now, Nasdaq's board is preparing for a succession to its long-time CEO, Bob Greifeld. Reuters has learned that he and the board have assembled a list of candidates.

Sources say the board has debated possibly splitting up the company or merging it with another to boost its valuation. And a merger with the London or Singapore stock exchanges would solve the succession issue by having LSE CEO Xavier Rolet or Singapore Exchange CEO Magnus Bocker take over Greifeld's corner office.

Other names on the list include former CME CEO Craig Donahue, TMX CEO Tom Kloet, ex-Nasdaq CFO Adena Friedman, former Nasdaq executive Chris Concannon, and Concannon's replacement at Nasdaq, Eric Noll.

Since Greifeld took office ten years ago, Nasdaq shares have quintupled , far outperforming the rival NYSE Euronext. They're getting a slight lift today. But the valuation of those shares is about half that of some other leading exchanges..

Nevertheless, Nasdaq signed Greifeld up for another five years last year, and sources say he has no plans to step down.