An expression attached to the masu-stem of a verb meaning 'very unlikely to ...; showing no sign of ...'.
このままでは、試験までに問題を全部覚えられそうもない。
At this rate, it's very unlikely I'll memorize all the problems before the exam.
雨雲が厚くて、今日は洗濯物が乾きそうもない。
The clouds are thick; the laundry is very unlikely to dry today.
彼は納得しそうもないから、説明を続けたほうがいい。
He doesn't look like he'll be convinced, so it's better to continue explaining.