I don't like your sentence as you've written it, using the word "meet" in what is, I guess, some form of the present tense.
However, I think you can rewrite it as "I haven't met someone I really like," or "I haven't yet met someone I really like," or "I have yet to meet someone I really like." These sound right to me, and the choice of "someone" feels natural and conveys a different meaning from "anyone."
Here, you would be using "someone" to carry the idea of a destined soulmate, the one person who is right for you. "I haven't met anyone I really like" carries the idea of there are "many fish in the sea," many possibilities, but I haven't found any of them yet.
This use occurs in the stock phrase "that certain special someone." A similar use is common in dozens of song lyrics; the first one that comes to my mind is a Gershwin song of the 1940s:
"There's a somebody I'm longing to see,
I hope that he
Turns out to be
Someone to watch over me."