Access to the platform formerly known as Twitter has been blocked in Brazil since the end of August, following an order by Supreme Court Justice Alexandre de Moraes.
The judge and the US tech firm have been at loggerheads over his investigation of "digital militias" he has accused of spreading hate messages in Brazil.
The dispute led X to close its offices in the country and let go of employees including its legal agent, breaching a local law.
The platform may again be available to Brazilians as early as next week after X provides documents requested by the court proving it now has a legal representative in the country, said the sources familiar with X's plans.
X and the Brazilian Supreme Court did not immediately respond to requests for comment.
Last week, X lawyers said the company had appointed a legal representative in Brazil, as ordered by the Supreme Court, but it did not initially provide documents to prove the appointee was formally able to respond for the company. Once the new set of documents have been sent, the firm expects the issue to be resolved, according to the sources.
The sources said X has also started to comply with the court's other demands - blocking profiles of people allegedly spreading fake news and paying a 18 million reais ($A4.4 million) fine via accounts of Musk's Starlink.
The social media firm is keen to smooth over the relationship with Moraes and operate like any other tech company in the country, said one of the sources.
