This morning, the board issued a press release saying they're in the midst of a CEO search and that they'd only consider people who would be a full-time CEO for Twitter. As Dorsey is already CEO of Square, and has told Re/Code that he will keep that job, it would appear the Twitter board is ruling out Dorsey as a candidate unless he quits Square.
Twitter has always given the appearance of a poorly-run company.
Longtime investor Chris Sacca said as much in his long blog post published a week and a half before Costolo stepped down. More recently, Sacca criticized Twitter's CEO search, saying that so far it has been poorly handled.
Two weeks ago, when Twitter announced that Dick Costolo would be stepping down as CEO on July 1 (that's next week!) they named co-founder Jack Dorsey as interim CEO. He appeared, along with Cosotolo the next morning on CNBC, to answer questions, but instead drew more attention about the size of his beard.
During the interview, David Faber and other CNBC reporters asked Dorsey several times if he could possibly be the full-time CEO of Twitter. Each time, Dorsey deflected, saying he wasn't thinking about that now. The non-denial signaled to many that he was interested in the job.