very unlikely to~; showing no signs of~
Describes that something seems very unlikely to happen or shows no signs of happening.
This pattern is used to express a strong negative prediction based on appearance or evidence. It's like saying 'it doesn't look like it will...' or 'there's no sign of...'. For example, if the sky is clear but you're worried about rain, you might say 雨が降りそうもない, meaning it looks very unlikely to rain. It can also describe a person's state, like 彼は元気そうもない (he doesn't look well). The pattern is more emphatic than just そうにない, and it often carries a nuance of disappointment or concern about the negative outcome. You'll hear it in both casual and formal speech, but it's especially common in spoken Japanese when commenting on situations. Note that for verbs, the ます-stem is used, not the dictionary form. Also, unlike そうだ (appearance), this pattern is not used with nouns directly.