Amman estimates that it has taken in close to 1.3mn refugees from its war-torn neighbour since the war in Syria broke out in March 2011, and spent more than $10bn to host them.
About 650,000 Syrian refugees have registered with the United Nations in Jordan.
The security source, who spoke to AFP on condition of anonymity, said that since the Jordan-Syria border reopened on October 15 “around 28,000 Syrians have returned home voluntarily”.
“They include around 3,400 Syrians registered as refugees with the United Nations.”
Known as Jaber on the Jordanian side and Nassib in Syria, the border is a key Middle East trade route and its reopening after a three-year closure was seen as a boon for the economies of both countries.
It was closed when rebels fighting the Syrian regime overran it in April 2015.