The Twitter logo on the front of the New York Stock Exchange (NYSE) in New York, when Twitter first went public, in 2013.  (AFP PHOTO/EMMANUEL DUNAND)

Twitter shares are way up in Tuesday trading, and not because people really like the new design of its tweet-quoting feature. 

Rumors are flying after numerous press reports, including one from Barron's citing "chatter" that Twitter is fending off a takeover bid. According to Barron's Tiernan Ray, that "unsubstantiated chatter" has also identified Goldman Sachs as the advising firm Twitter's hired to keep takover offers at bay.

Twitter declined to comment.

The company's shares closed nearly 4 percent up  to $52.87 per share. The stock opened at $51.01 and went as high as $53.28 on the admittedly sketchy reports.

This is not the first time there's been talk of a Twitter takeover. It's been batted about for years, well before Twitter went public, and the idea resurfaced as recently as January that Google might be the suitor in question. Google has again been named as a possible buyer in this latest round of rumors; the company declined to comment on rumor and speculation.

Twitter's had some problems growing its audience since going public, which it's addressed by revamping the site's design to make it easier for newcomers to understand. The company's board has also stood staunchly behind  Twitter's chief executive Dick Costolo as he's looked for ways to profit reliably from all those 140-character messages.

There's also the question of which of the major tech companies could possibly buy Twitter without alienating its core, dedicated audience. The social network has its own character -- for good or for ill -- and one that doesn't fit in with the more-mainstream personalities of Facebook, Google and Microsoft. Anyone who might buy Twitter with an eye to keeping the service's users will have to tread very carefully indeed.

Then again, none of this beyond the giddy rumor stage, even if it does move markets. So take the reports with as much salt as you'd like.