The surprise departure of Twitter CEO Dick Costolo on Thursday has triggered a range of reactions from the analyst community, including the prospect that the move essentially sets up the company for a sale.

In a joint press conference with incoming interim CEO Jack Dorsey, Costolo played down that very suggestion but didn’t entirely rule it out either. “We’re absolutely committed to maximizing value for shareholders,” he said. “We see no reason we can’t do that as an independent company.”

But Jefferies Equity Research issued a research note Friday declaring that the leadership change could increase the probability that Twitter is sold. “During the interim search period we believe the opportunity for acquisition is heightened (and would likely require a valuation of $30B+),” said analysts Brian Pitz and Brian Fitzgerald. “The lack of a CEO successor signals to us the potential for acquisition.”

The prospect of Twitter being put on the block is hardly a new one. Just a few weeks ago, as part of a lengthy critique of the company’s strategy, venture capitalist Chris Sacca held out the possibility that such a deal could be struck, mentioning Google and Alibaba as potential suitors.

Barclays analyst Paul Vogel questioned the timing of Costolo’s announcement, which he characterized as “somewhat surprising given the proximity to the end of the quarter. Also, the immediacy of Mr. Costolo’s departure raises our eyebrows as he will relinquish the role to co-founder Jack Dorsey rather than remain on himself, despite the fact that the search process has not yet begun.”

But Cowen & Co. analyst John Blackledge wasn’t surprised by the succession, citing all the criticism that had been mounting regarding Costolo. While he credited the CEO for building a strong track record for Twitter on the product side, he held out the possibility of future improvement under new leadership.

“There is more work to be done on the product offering to drive engagement and user growth, as well as work on building or partnering on the advertising side to effectively compete vs existing and emerging social and digital platforms and continue fast-paced topline growth,” he said.

J.P. Morgan analyst Doug Anmuth thinks Twitter will end up looking outside the company for fresh blood in the top job. “We believe an external candidate is far more likely to become CEO, and we believe the search will focus on executives with strong product and engineering experience, though we would not rule out those who have been more advertising and monetization focused,” he said.

Another area where the new Twitter CEO will be able to help is Wall Street, which Pivotal Research Brian Wieser believes needs to come to a better understanding of how early the company is in its development and where its strengths truly lie.

“We do think that whomever is running Twitter going forward will need to focus its dialogue with the investment community on the commitments they know they can meet and on areas in which they have been successful, like commercial traction with large brands and what seems to us to have been a number of clever strategies to support a strong long-term position within the advertising industry,” he wrote. “More clarity on emerging revenue stream segments will be helpful, too.”