Never has been stated one way or another, but Littlefinger did allude to there being more to the kidnapping than it seemed. So we're all left guessing.
Yeah, I bet he knows that the whole kidnapping story Robert tells is a bunch of bullshit and Lyanna actually ran away with Rhaegar but if I had to bet, I'd say he doesn't have any clue that Jon isn't Ned's kid. Also, he probably would've played that piece long ago when he was trying to get the Lannisters and Starks against each other. What better way to add even more fuel to the fire than to pit Robert against Ned?