That form is very popular using form of korean '~(Verb)할 것 같습니다'
'할 것', '~을 것' These are mean 'occur in near future'
syn ' be going to'
'같습니다' is self-prediction of doing oneself.
syn 'feel like', ' would like to'
So, In summary I'll show you structural analysis with completed answer.
I feel like ( I'm) going to cry
나(는) ~ 같습니다 doubled Subject ~(할) 것 울다
But directly connect these vocabularies, it isn't natural form of korean sentence.
Normally ( ) is unnecessary thing but Help your apprehend structure, I'll remain it
나는 울(다)(~할) 것 같습니다 -. 나는 울 것 같습니다
cf. '잃'다(conjugated form like 잃을 잃으니(깐) etc) korean verb mean losing it.
'잃' is core part of verb, So I want to stress on it. If you check out Korean Grammar book, there are many usages of verb extension.