The company will likely need someone with product and advertising experience, the RBC Capital Markets analyst said on CNBC’s “Squawk Box.” The candidate should also have held the top spot at another public company, Mahaney added.
“That makes it a pretty short list of people who could come in and turn this around, and it also is going to take quite some time,” he said. “That’s probably a year, year and a half turnaround. It’s a very hard job.”
For that reason, Mahaney does not recommend the stock.
To be sure, the role presents an opportunity for the right person, he said.
“Some people talk about Twitter being niche. Come on, it’s 300 million people. It’s still growing reasonably year over year,” he said.
Twitter announced Thursday Costolo would leave his post on July 1. Twitter co-founder and Chairman Jack Dorsey will be interim chief executive while the company searches for a replacement.
The social media company had been under pressure from shareholders to replace Costolo for some time. Investors worry about the company’s ability to grow its user base, and advertisers appear unconvinced Twitter can produce meaningful return on investment, RBC Capital Markets said in a note.
Sources told CNBC Costolo made the decision to leave the position, and had been considering it for a while. Costolo will remain on the board of directors, which includes two other former CEOs, Dorsey and Evan Williams.
That creates a potentially awkward situation for an incoming CEO, said Mahaney. The new chief would likely want to hold the chairman position, as well, he added.
Read MoreNo long-term cheer for Twitter stock
“This is a company and a brand that’s got ubiquitous reach, but a lot of execution challenges,” he said. “I’ve never seen as much C-level turnover in a company 18 months post an IPO as you’ve got now with Twitter.”
The company has also replaced its chief operating, financial and marketing officers.
Some market watchers have speculate that current CFO Anthony Noto, who has a Wall Street background, could replace Costolo.
“It’s probably most likely to be a product person, somebody that can convince the mainstream what do you use Twitter for. How do you keep regular people coming back to Twitter?” Anthony DiClemente, managing director at Nomura Securities, told “Squawk Box.”
Twitter has lost share in the market for conversational technology due to the rise of messaging apps, DiClemente said, noting that Twitter has just over 300 million users, while Facebook‘s Messenger has about 500 million and its subsidiary Whatsapp boasts more than 700 million.
The world has come to view Twitter as a broadcast medium, turning to the social network during crises and breaking news events, he said. While that has value, it also makes it somewhat of a niche product, he explained.
“Most of us would like to connect with our family and friends. And that’s the use case for Facebook,” he said. “Twitter has got one-fifth the users of Facebook. How do you broaden the use case?”
While Facebook reportedly expressed interest in buying Twitter long ago, Twitter’s valuation has come a long way, DiClemente said. Twitter’s market capitalization is $23.5 billion.
Another talked about buyer, Google, already has a search engine and advertising partnership with Twitter, and so it may be content to continue “leasing” Twitter, he said.
Monetization is decelerating and ad growth “hit a wall” in the first quarter, raising questions about how much advertisements are engaging Twitter users, he added
“The question is, because of the volatility in leadership, is it worth more in the hands of somebody who has a greater pool of advertisers to draw from, who has better ad technology?” he said.
The chance of Twitter being acquired are very slim because there is no obvious buyer except Google, and that deal would face significant regulatory challenges, Mahaney said. A long regulatory review could create roadblocks to growing the company, he added.