〜そうにない・〜そうもない
doesn't look like it will
Verb ます-stem + そうにない / そうもない
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The negative of the N4 そうだ ("looks like it will") is そうにない or そうもない: この雨はやみそうにない, "this rain doesn't look like it'll stop".
It attaches to the ます-stem, just like the positive: 終わりそうもない, 来そうにない. The polite forms are そうにありません and そうもありません.
そうもない is a little more emphatic: "not the slightest sign that…".
The form そうじゃない means something different: "not like that", or "doesn't look (adjective)", as in 難しそうじゃない. For verbs predicting what will happen, use そうにない.
It often comes with potential verbs: 解決できそうにない, "it doesn't look like it can be solved".
Examples
この雨はやみそうにない。
This rain doesn't look like it'll stop.
今日中に終わりそうもない。
It doesn't look like I'll finish today.
彼は来そうにないね。
It doesn't look like he's coming.
この問題は簡単に解決できそうにない。
This problem doesn't look like it can be solved easily.
今年は休みが取れそうもありません。
It doesn't look like I'll be able to take any time off this year.