expression, auxiliary
Negative conjecture form of だ/である, expressing that something does not appear to be the case. Often used after nouns or na-adjectives. The では is a contraction of で + は, and なさそう is the negative stem of ある with the conjectural そう.
See also: じゃなさそう
He does not seem to be a student.
This problem doesn't look easy, does it?