According to the paper the issue came to light when the US military in Iraq apprehended a fighter whose laptop contained files of intercepted drone video feeds.
In recent months the US military has also reportedly found evidence of at least one instance where fighters in Afghanistan also monitored US drone video feeds.
The interception is possible because communications links with the remotely flown planes are unprotected.
Officials said when the intercepts were discovered in July last year, the Pentagon began a programme to start encrypting all of its drone video feeds from Iraq, Afghanistan and Pakistan.
However, there are at least 600 unmanned vehicles along with thousands of ground stations to address and the upgrade is expected to take some time to complete.
Dale Meyerrose, a former chief information officer for the US intelligence community, compared the problem to street criminals listening to police scanners.
"This was just one of the signals, a broadcast signal, and there was no hacking," he told the Associated Press.
The US Predator drone, also currently used in Pakistan, Somalia and elsewhere, can fly for hours remotely controlled by pilots thousands of kilometres away.
It can fly armed or unarmed, and is part of a growing arsenal of such aircraft that includes the Reaper and Raven as well as a new, high-tech video sensor system called the Gorgon Stare, being installed on Reapers.