The sources told dpa that Syrian air defences were activated early Tuesday, but that it turned out to be a false alarm.
Syrian state-run news agency SANA had reported that air defences had intercepted some of the alleged missiles. Similar reports on state-run television were later pulled from news bulletins.
The airbase is the same one struck by the United States last year in response to a sarin gas attack on the rebel-held town of Khan Sheikhoun in north-western Syria, in which more than 80 people died.
The US, Britain and France launched coordinated strikes on Syrian government targets on Saturday, following an alleged chemical attack on the town of Douma, outside Damascus on April 7.