When Twitter Inc. (TWTR) announced that CEO Dick Costolo will step down on July 1, the news was met with a mixture of surprise, delight and concern. Interestingly, just a couple of weeks ago, Costolo was not concerned about his job security. When asked about it at the Re/code conference, he said he wasn't worried because he and the board were "completely in sync."

One of the rumors that's been following the company around for a while now was that it's being pursued as an acquisition target by various suitors. So will the acquisition rumor come to fruition now that the top post is essentially empty? Some analysts seem to think so, but not all are convinced.

Is a Twitter acquisition likely?

Deutsche Bank AG analyst Ross Sandler and his team suggest that now it seems a little more likely that Twitter will be acquired by another company. They have a Buy rating and $60 per share price target on the micro-blogging company.

The Deutsche Bank team said the departure of Costolo, when taken with the lack of a super-voting share structure, a board that's "somewhat on the defensive," the high value of its assets, and the "current environment of cheap money," suggests that the likelihood of an acquisition is slightly greater now. Despite this view, they're not "playing for that outcome."

Jefferies analysts Brian Pitz, Brian Fitzgerald and their team also suggest that Costolo's departure may make an acquisition of Twitter more likely. The reason for this is because Twitter did not name a replacement when it announced that Costolo was stepping down. They suggest that the situation could be "a setup for a 'strategic investor or buyer' to step in."

No Twitter acquisition, say some

Bank of America Merrill Lynch analysts Justin Post and Joyce Tran disagree, saying that they don't think many companies would even be interested in acquiring Twitter. The one possibility they see is Google Inc. (GOOG), which has been rumored to be considering making an offer for the micro-blogging platform. However, they also see regulatory challenges to such a combination.

Macquarie analyst Ben Schachter sides with BAML, staying that there's no indication either way. They say an acquisition of Twitter has been a possibility for some time and simply remains a possibility. However, they add that an acquisition would present the biggest bull case possible for Twitter.

What kind of CEO would Twitter need?

So if Twitter does not get acquired, then who would make a better CEO for the struggling company? JPMorgan Chase & Co. analyst Doug Anmuth and his team believe that an outside candidate is more likely to win the top spot at Twitter. They expect Twitter to focus on executives who have strong experience in products and engineering, a view that BAML analysts also hold. However, they also think it's possible that executives with experience in monetization and advertising will be strongly considered.

The Jefferies team suggests that Twitter needs a CEO who will focus more on user growth rather than monetization because investors have been so concerned about user growth. They noted that Costolo hasn't been able to increase Twitter's logged-in user base.

Further, the Jefferies team thinks Twitter's next CEO should leverage assets like Periscope, Instant Timeline, Logged-Out Homepages and the new deal with Google to convince logged-out users to log in. They have a Buy rating on Twitter.

Morgan Stanley  analyst Brian Nowak and his team have a sentiment that combines the idea of a product specialist with a user growth specialist. They suggest that Twitter needs "a product specialist laser-focused on emphasizing and building Twitter's core use case.