In a sign that shareholders want value from their investment in Twitter, the company's board of directors have sent a blunt message to one of the expected likely candidates to take the social network's top job after Dick Costolo announced that he would be stepping down from the CEO role.

The social micro-blogging company's search committee will only consider CEO candidates "who are in a position to make a full-time commitment to Twitter," the board said. That would seem to rule out Jack Dorsey, the company's cofounder who currently works as the CEO of Square and will be filling in as interim CEO of Twitter.

Burning the midnight oil at Twitter HQ in search of a new CEO. Image: Twitter
Burning the midnight oil at Twitter HQ in search of a new CEO. Image: Twitter

Dorsey has said that he plans to remain at the helm of the payment processing company he cofounded, but hasn't explicitly ruled out a bid for a permanent berth in Twitter's top job. Now the Twitter board has made it clear that he would have to depart Square if he wants to run Twitter. That's a rough proposition for Dorsey, especially since Square is reportedly planning to go public this year.

As for the overall search process, Twitter's search committee has contracted with executive search firm Spencer Stuart to evaluate internal and external candidates for the job. The board hasn't set a firm time frame for its hiring of a new CEO, saying that there's a "sense of urgency" to the process but that it will take its time to find the right person for the job.

Whoever steps into the top spot at Twitter will have to contend with increased pressure on the company from Wall Street. Investors have been disappointed by Twitter's revenue and user growth in recent quarters.