I'm thinking flirting. All them nice words, smiles, eye contact and pushyness. Didn't Mon-El find out he's dying? Isn't that the perfect time for "Time is running out, and I've never really experienced much, certainly not luuuv, oh hey here's this cute guy, maybe I'll experience some love and then die in his arms or go off into another dimension never to see him again".
Then again the "don't be a stranger"-comment is a bit of a "shoo, go away now". Unless of course Monny is on his way out there.
I would like to point out my knowledge of Mon-Els backstory is limited at best, and don't know if he's ever been romantically linked with anyone.