そうにない

Doesn’t seem like/Unlikely to
Verb ます stem + そうにない

そうにない is used to express the opposite of そう(Seems like), with verbs. 
Nouns should still use じゃなさそう. 
そうに here is the adverbial form of そう, which is a な adjective, modifying ない (“not).
That is to say, そうにない means “Doesn’t seem like”.  It indicates a judgment of low possibility.

そうにない tends to be (Not exclusively) used in situations contrary to expectations, hope or effort. For example:

• 今日は降りそうにない – It doesn’t look like it’s going to rain today. 

Is a statement you’re not likely to make without either expecting rain or hoping for rain, or being asked (someone else expected). 

Examples

• クリスマスなのに雪が降りそうにない – Even though its Christmas, it doesn’t look like it’s going to snow.
• 好きになりそうにない – Doesn’t seem like (I’ll) come to like it. (Was trying, hoping, or expecting).
• 退屈しそうにない – Doesn’t seem like I’m going to be bored. (Expected boredom).
• 水を与えていないが、かれそうにない – I’m not giving it water, but it doesn’t look like it’s going to wither. 
  
  

そうもない and そうにもない

そうもない is another variation of this phrase. Since も is the emphasis particle, this sounds slightly stronger than そうにない, i.e. less likely. (Source)

• 今日は終わりそうもない – Doesn’t seem like it’s going to finish today.
• 彼は頑張りそうもない – It doesn’t seem like he’s going to try.

Additionally, そうにない is slightly more objective, while そうもない is slightly more subjective. (Source)

そうにない was originally そうにもない but you’ll rarely see it these days. If you do, it has an even stronger meaning than そうもない (I.e. very unlikely). (Source)

• できそうにもないことを頼んだ – He asked something that doesn’t seem possible to do. 

Potential form + そうにもない is quite strong, so when used it kind of feels like “Obviously doesn’t seem possible”. Most likely to be a criticism of something unreasonable.  

• 食べそうにもない量を取るなんて、もったいないことする. – Taking more than you could possibly eat is wasteful.