You cannot break it up as
since Japanese does not allow postpositional phrases to modify nouns without a の. So the phrase should be parsed
You might find it strange that the 君に modifies ある, not 話, since in English the most natural parse would be "I have a [present for you]". However, English actually also allows the above parse, e.g. "[For you], I have [a present]". This might help you to understand the Japanese parse intuitively.
What if you wanted 君に to modify 話 instead? Syntactically you could, turning it into
(にの is not allowed, and becomes への), but this is not very natural. The reason is that these postpositional phrases with の mostly modify definite nouns, and do not work well with 話, which is indefinite (a story, a talk).
However, changing the noun a bit, you could construct a meaningful pair highlighting the difference:
君にプレゼントがある I have a present (indefinite) for you
君へのプレゼントはあそこにある My present for you (definite) is over there