No reason was given for the shake-up, which came as government forces have made little progress in a two-month-old offensive against rebels in the northwestern Idlib province despite recapturing wide areas of the country in recent years.
There was no immediate confirmation from the government or state media, which rarely report news related to intelligence agencies.
Several pages, including Latakia Eagles and Homs Network Live, reported that Hassan was replaced by his deputy, Maj. Gen. Ghassan Ismail.
Hassan was one of 13 Syrian commanders and prison officials that the United States said in 2016 were responsible for attacks on cities, residential areas and civilian infrastructure as well as acts of torture. The U.S. and the European Union had imposed sanctions on Hassan because of his role in the crackdown.
Last year, Germany said it is seeking Hassan's arrest, saying his intelligence agency was suspected to have been involved in war crimes.
Earlier this year, there were reports that Germany asked Lebanon to hand over Hassan while he was being treated in a hospital run by the militant Hezbollah group, which has sent fighters to Syria to help Assad's forces.
The pages said the General Intelligence Directorate is now headed by Maj. Gen. Hussam Louqa, while Maj. Gen. Nasser al-Ali is now in charge of the Political Security Directorate. Bahjat Suleiman, a former intelligence chief and former ambassador to Jordan, also listed the names on his Facebook page and Twitter account.