Twitter shares rise amid Google acquisition rumors

Should Google buy Twitter?
Should Google buy Twitter?   

Twitter shares were up Thursday amid renewed speculation that Google may be interested in the social media company.

"It's not lost on Google that Twitter is the best real-time search engine out there…there has been speculation as far back as 2009 that Google would buy Twitter from valuations of $10 billion to $20 billion pre-IPO," SunTrust's Bob Peck told CNBC's "Fast Money Halftime Report."

Peck said that the perennial rumor would likely "take north of $40 billion" to accomplish, and would be difficult although not impossible to achieve.

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Twitter shares were up 3.3 percent in midday trading.

"It would be tremendous amount of leverage, obviously, having Twitter disseminated across all of Google's products." Peck added.

Twitter and Google both declined to comment.