The beef between Pusha T and Drake may hinge on whether Drizzy fathered a child with French porn star Sophie Brussaux.

Drake's peeps are pushing back on that possibility.

Sources have told TMZ that Drake has been hit with many paternity claims over the years, including from women he didn't have sex with. They have so far all been proven false.

Drake does think there's a chance he knocked Brussaux up.  Which is why he's been paying her support after initially ignoring her claim. But TMZ's sources insist that there hasn't been a DNA test yet because Brussaux has trouble getting into the United States and Drake hasn't had time to travel. But they believe there will eventually be one.

The sources also question if the baby boy is Drake's, as it's said to have blonde hair and blue eyes.