A colloquial contraction of 'ではなさそう', meaning 'doesn't seem to be ~' or 'it appears not to be ~'; commonly used in conversation.
彼は学生じゃなさそうだ。社会人に見える。
He doesn't look like a student. He seems like a working adult.
今日は雨じゃなさそうだから、傘はいらないと思う。
It doesn't look like it's going to rain today, so I don't think we need umbrellas.
その情報は正確じゃなさそうだから、別の資料で確認しよう。
That information doesn't seem accurate, so let's check another source.