Less than two weeks after Dick Costolo thrilled Twitter’s shareholders with the news that he was quitting his role as the social media service’s CEO, the company’s board of directors has made a statement that undermines the candidacy of one of the front-runners to be his replacement.

Twitter’s search committee, led by former Netscape Communications CFO Peter Currie, has said the social media network will only consider applicants who are “in a position to make a full-time commitment to Twitter”. Which means that the current interim CEO, Jack Dorsey, who is also the CEO of payment processor firm Square Inc., would seem to have a bit too much on his plate to make the position permanent.

At the time Costolo announced his departure, Dorsey played down the challenge of steering two ships at the same time, saying that both companies have strong enough leadership teams that it wouldn’t be a problem to combine the two roles. He also said that he has no plans to quit his job as CEO of Square, a company which he co-founded, but at the same time he didn’t rule out bidding for the Twitter job in a permanent capacity.

Essentially, what Twitter’s board seems to be saying is that Dorsey must quit Square if he wants to take on Twitter full time. It won’t be an easy decision for Dorsey given that Square is reportedly planning to launch an IPO later this year.

At least Dorsey should have a bit of time to decide what he wants to do. Twitter has said it’s contracted the services of executive search firm Spencer Stuart to help it evaluate internal and external candidates for the CEO job. The company admits there’s a “sense of urgency” to finding a new CEO, but says it won’t be rushed into finding the right person to lead it.

As far as Dorsey’s rivals for the job go, Business Insider says that Instagram co-founder Kevin Systrom and Yahoo! Inc. CEO Marissa Mayer are at the top of the shareholders’ wish list, while Twitter’s interim CEO Dorsey, Global Revenue President Adam Bain, CFO Anthony Noto, and SVP of Product Kevin Weil are the main internal candidates.

Whoever does land the top job will certainly have his hands full, being forced to contend with increased scrutiny from shareholders who’ve made no secret of their disappointment at Twitter’s recent revenue and user growth.

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