Mr Assange has been holed up for more than five years in the Ecuadorean embassy in London where he was granted asylum in 2012 to avoid extradition to Sweden over rape allegations.
Swedish prosecutors in May dropped their investigation into the rape allegations, but British police have said Mr Assange would still be arrested if he left the embassy.
Reuters found an entry for "Julian Paul Assange" in Ecuador's Civil Registry, which only includes Ecuadorean citizens. A spokeswoman for the registry declined to comment when asked if Mr Assange had been granted citizenship.
Following reports of the news in Ecuadorean media on Wednesday, Mr Assange tweeted a photo of himself wearing the jersey of Ecuador's national soccer team. Neither he nor his lawyers responded to requests for comment.
On Tuesday, Foreign Minister Maria Fernanda Espinosa said Ecuador was exploring mediation to solve the standoff.
Mr Assange, who denies the rape allegations, fears that if he is arrested he will be handed over to the United States to face prosecution over WikiLeaks' publication of thousands of classified military and diplomatic documents in one of the largest information leaks in U.S. history.
(Reporting by Alexandra Valencia in Quito and Mark Hosenball in London; Writing by Brian Ellsworth; Editing by Sandra Maler)