Has this phrase really been transliterated from existing letters?
It cannot be interpreted according to th Korean grammar easily.
I guess it is one that was written by an English speaker translated one word by one word.

It might be interpreted as following:

nae-ga : I
sa-rang : Love
tang-sin : You

But this disregards the Korean grammar.

The Korean language has a type of SOV, while the English SVO.
Moreover, the Korean uses different forms of words when the parts of speech are different.

If you want to say "I love you" in Korean, you can say it by combinating the following phrases.

I (nominative form of the pronoun of the first single person) :
na-neun (casual; most ordinary)
nan (casual, rough)
jeo-neun (formal)

you (accusative form of the pronoun of the second single person) :
tang-sin-eul (formal)
neo-reul (casual)
neol (casual, rough)

love (present form of the verb) :
sa-rang-ham-ni-da (formal, polite)
sa-rang-hae-yo (casual, polite)
sa-rang-hae (casual, impolite)

For example:

na-neun tang-sin-eul sa-rang-ham-ni-da.
nan neol sa-rang-hae.
etc.

NOTE : The m-sound in "ham" above is written with p-sign orthographically. This sound is under the influence of euphonic change from the following n-sound.