そうもない details

write + shows no sign of

kaki sou mo nai

shows no sign of; doesn't look like it will

meaning: show no sign of writing

今日きょう、太郎たろうはきそうもないな。

kyou, tarou wa ki sou mo nai na.

Taro shows no sign of coming today. casual

この空そらの様子ようすだと、雨あめは降りふりそうもない。

kono sora no yousu da to, ame wa furi sou mo nai.

Judging by the sky, it shows no sign of raining. neutral

Examples

shows no sign of; doesn't look like it will — predicts, from present appearance, that something won't happen

今日きょう、太郎たろうはきそうもないな。

kyou, tarou wa kisoumonai na.

Taro shows no sign of coming today. casual

この空そらの様子ようすだと、雨あめは降ふりそうもない。

kono sora no yousu da to, ame wa furisoumonai.

Judging by the sky, it shows no sign of raining. neutral

今回こんかいの交渉こうしょうは、簡単かんたんに解決かいけつしそうもありません。

konkai no koushou wa, kantan ni kaiketsushisoumoarimasen.

This round of negotiations shows no sign of resolving easily. neutral

そうにない — に replaces も — the plainer derivational negative; そうもない adds a mild "not even" emphasis and reads slightly more spoken

Both そうもない／そうにない are fully productive, irregular verbs
included: きそうもない, しそうもない.

そうだ
Both judge from how things currently look, but this isn't そうだ simply negated — 降りそうじゃない？ mostly surfaces as a rising-intonation confirmation tag ("looks like rain, doesn't it?"), not a flat declarative negative, which instead runs through this frozen そうもない／そうにない tail.