Twitter's shares, which rose as much as 14 per cent on Wednesday, pared some gains and closed up 4.1 per cent at $17.38.
The stock rose from a record low after unconfirmed chatter about News Corp's interest in Twitter circulated on Wednesday. The rumours intensified after a CNBC segment, tech website Re/code said.
The social media site was evaluated as a takeover target because of the company's shrinking stock price, Re/code said.
In the few months since co-founder Jack Dorsey returned as the chief executive, Twitter has been trying to make the site more engaging. The company said in December it was testing a feature to show ads to people who read tweets without logging in as it tries to monetize non-active users.
"Twitter inside a larger organization definitely makes theoretical sense, whether its another internet company or a media company," Monness, Crespi, Hardt, & Co Inc analyst James Cakmak said.
A News Corp spokesman said there was no truth to the rumours.
Twitter already has several high-profile investors. Former Microsoft Corp CEO Steve Ballmer reported a 4 per cent stake in October, making him the third-biggest shareholder after Twitter co-founder Evan Williams and Saudi billionaire Prince Alwaleed bin Talal.
Twitter has been the subject of takeover rumours in the past, including a fake report attributed to Bloomberg that claimed the company had received an offer to be acquired for $31 billion.
Twitter had received bids from Alphabet Inc's Google and Facebook Inc, according to reports.
Twitter trades at 28.12 times forward earnings, below its peer median of 36.06. Facebook has a PE of 33.08, while LinkedIn Corp's is 52.64, according to Thomson Reuters data.
"Even though News Corp denied the rumours, I do think this could help investors potentially see some valuations for the stock," Cakmak added.
Up to Tuesday's close, the stock had fallen nearly 41 percent since Dorsey was named permanent CEO in October.