"잔 것 같아" The expressions for 것 같아(it looks like, it seems) are: ~ㄴ 것 같아: looks like (someone has done something / is in certain state). Ex: 잘된 것 같아. ~는 것 같아: looks like (someone is doing something). Ex: 잘되는 것 같아. ~ㄹ 것 같아: looks like (someone will be doing something / will be in certain state). Ex: 잘될 것 같아. So 잔 것 같아 most likely means "(someone) looks like he/she has just slept". But it is more common to say "(금방) 자고 일어난 것 같아" (looks like someone has just got out of bed). 잔 것 같아 can also mean "It looks like they have slept together" (걔네 같이 잔 것 같아) if it's in such a context.

Guessing (someone) slept 자다(sleep) + ~ 한 것 같다(looks like or guess)