Some have speculated that Jack Dorsey, Twitter’s interim CEO during the search, already has the job locked down.

Whoever Twitter chooses, the incoming CEO will face a daunting board that includes three former CEOs: Williams, Dorsey, and Twitter’s most recent CEO, Dick Costolo. When asked about that potentially awkward situation at Fortune’s Brainstorm Tech conference in Aspen today, Williams said he would be willing to step down if the new CEO preferred to have fewer former CEOs watching their every move.

“The board composition won’t be a deciding factor in the choice,” Williams said. “I will say personally if the right CEO would prefer one less CEO on the board, I would be happy to…” He trailed off, concluding: “It’s more important that we get that person than I’m on the board.”

Williams outlined the board’s desire to find “an exceptional leader,” who has a “defining vision” for Twitter and “can make things happen.” Costolo was frequently knocked for his lack of a clear vision for the Twitter product, and the fact that he cycled through multiple heads of product during his tenure. But Williams said product know-how isn’t as important as strategic vision for the new CEO. “There are lots of amazing product people within Twitter and the potential is so vast and always has been,” he said. “The real challenge is deciding what to focus on and aligning the entire organization toward that purpose.”

While noting that it wasn’t his place to define Twitter’s strategy, Williams said the company has the most potential as a source of realtime news. “Twitter excels at that,” he said, noting that Twitter could improve the way it organizes information and helps people find what they’re looking for. “I guarantee they have all the information you’re looking for,” he said. “What we’re building into Twitter is better ways to organize that information. It’s there. It’s absolutely there.”

During the interview, a fake Bloomberg news story was published that said Twitter (TWTR) had received a $31 billion takeover offer. The story was quickly shared, given rampant rumors that Google might be planning a bid. (This despite Google’s stated move away from social networking after the disappointment of its own social network, Google+.) The story was quickly revealed to be a hoax thanks to its URL — Bloomberg.market, not Bloomberg.com. But Twitter shares spiked before quickly returning to normal trading levels.

When asked if Twitter would be better off under the umbrella of a larger company or as a private company, Williams cited his fiduciary duty as a board member. “Blah, blah, blah, the board will do what it’s supposed to do,” he said.