Obviously the Thing wouldn't know who would be dreamt of, but...
Why would the Thing pick Menel:
Talks more, would be able to come on and defend himself from Eonwe. Already under suspicion, though not a lot and mostly from me (

), but has gotten over that suspicion.
Why would the Thing pick Eonwe:
Quiet, has flown far under everyone's radar so far. Not much for us to go on, has left very few clues and the Thing would have recognized that and kept it in mind when choosing who to pick last night.