CNBC, citing unnamed sources, said on Friday possible suitors include Alphabet's Google and Salesforce.com. No sale is imminent.
Twitter, Salesforce and Alphabet could not be reached immediately for comment. Salesforce shares fell more than 3 percent, while Alphabet dipped around 0.25 percent.
Twitter has been a near-constant focus of takeover speculation amid persistently disappointing sales and user engagement. In its most recent quarterly report, it posted its slowest revenue growth since going public in 2013 and issued a lacklustre outlook.
Co-founder Jack Dorsey returned to the company as chief executive in 2015, but his plan for reviving Twitter is at best seen as unfinished.
The CNBC report sent Twitter shares to their highest since early January. It last traded around $22.30 a share.
Twitter's stock regularly jumps on rumours that a bid is afoot, none of which have so far developed into a deal.