Bradley Cooper and Jennifer Lopez -- 'Casually Dating'

Bradley Cooper and Jennifer Lopez are not a couple just yet ... but a source close to the pair tells TMZ they are indeed "casually dating."

As TMZ first reported, the two went on a dinner date in New York City last month. They had not been spotted out again until yesterday -- when a photo surfaced of Bradley Cooper driving an SUV and a woman who certainly looked like JLo ... covering her face in the passenger seat.

According to our sources, the woman in the photo is definitely JLo. We're told the two enjoy each other's company but are keeping things simple for now.