そうもない・
Use this construction when the present situation gives you reason to think that an event is unlikely to happen. It expresses a negative outlook based on visible or situational evidence, not mere uncertainty.
A prediction from the situation now
The speaker sees unfavorable signs and judges that an event probably will not occur or be completed. Natural contexts therefore mention evidence such as slow progress, a long delay, continuing symptoms, or a search that has produced no clues.
The two main variants
The choice between the two variants rarely changes the basic prediction.
A small difference in emphasis
そうもない can sound more emphatic, roughly suggesting that the event does not look at all likely. This is only a tendency, however; do not treat the two forms as having separate fixed meanings.
Evidence-based outlook versus open possibility
そうもない・そうにない says that present signs point against an event. By contrast, かもしれない simply keeps a possibility open and does not require immediate evidence from the current scene.
More examples
三日たっても熱が下がらないので、明日退院できそうもない。
The fever still has not gone down after three days, so discharge tomorrow does not look likely.
Analyze手がかりがほとんどなく、原因はすぐには特定できそうにない。
There are almost no clues, so it does not look as though the cause can be identified soon.
Analyze窓口の前には長い列ができていて、昼までに順番が回ってきそうにない。
There is a long line in front of the counter, so it does not look as though my turn will come before noon.
Analyze電車が一時間以上遅れているので、会議には間に合いそうもありません。
The train is more than an hour late, so it does not look as though I will make it to the meeting on time.
Analyzeエンジンから変な音がしている。この車では目的地まで走れそうもない。
The engine is making a strange noise. This car does not look likely to make it all the way to the destination.
Analyze今の予算では、今年中にこの計画を実現できそうにありません。
With the current budget, it does not look as though this plan can be realized within the year.
Analyze