Probably the second choice - "I'm trying to place you." There is a small chance that "I keep trying to place you" would imply to the person that you're obsessed with them, that you have concentrated on them for a long time. A small chance, but a chance, nonetheless.

I personally just say something like: "You look familiar..." "I know your face from somewhere..." "Where do I know you from?" "I know you but I can't picture where from..." I've personally never used the word "place" in this context, nor have I ever heard anyone else use it. I say this to provide an alternative cultural perspective.

u can probably say: do i know you from somewhere? well...I can't place you

Can you give me aDetailed explanation?

You look familiar, but I can't place. I can't quite place you. We don't say: "I'm trying to place you."