The source told CNN that Qureiris, who was arrested by Saudi authorities at the age of 13, could be released by 2022. He had to stay in jail for three years.
CNN has asked the Saudi government for comments.
International pressure on the kingdom had increased after CNN reported the case of Qureiris.
In Austria, the country's parliament voted to close a Saudi Arabia-sponsored inter-religious dialogue center to protest the imprisonment of Qureiris.