Wikileaks say U.S. investigators have served subpoenas for the information at Twitter's San Francisco headquarters.
They reportedly want private messages and other personal details from the accounts of founder Julian Assange and three others associated with Wikileaks.
U.S. officials have been examining possible charges against the website after a series of leaks that embarrassed officials and damaged Washington's image.
Twitter has not commented on the claims. Wikileaks says it plans to fight the subpoena.