"Nehledám na tebe." could be roughly translated as "I am not searching ON you.", which is, simply, wrong. "Nehledám tebe.", on the other hand, could be translated as "I am not searching for you.", which is the correct option.
I can't provide any more information, because I am not Czech myself, but Slovak and our languages are so similar that we are mostly able to spot mistakes in a sentence (grammatical, orthographical, etc.).
As a native Czech speaker I confirm, that @ValaMorg is correct :) You simply cannot say "Nehledám na tebe" it does not make any sence, whereas "Nehledám tebe" is correct.
I always try to remember that some words like hledám already have the preposition attached. I think of hledám is looking for and try to remember it that way.
And in addition to others, "nehladám" is a typo/misspelling. The correct spelling is "nehledám".
A few additional notes (I hope I will not just raise confusion):
1) "Nehledám na tebe." does not make much sense, however, (as I consider to be rather advanced Czech), it is possible to say for example "Nic na tebe nehledám." The meaning of "Hledat něco na někoho." is to search for some dirty information about someone in order to use it against him (for example in politics).
2) A bit more natural would be to use Locative instead of Accusative: "Nehledám na tobě." That means that I am avoiding you during the search: "I don't search on you."
3) If you literally translate "I don't search for you." to "Nehledám pro tebe.", the sentence still makes kinda sense but the meaning is different. It would mean that I don't want to give it to you after I find it. However, I would still expect an object in the sentence: "Nehledám to pro tebe."
Two little clarifying questions on your very useful comment, if you have a moment...
1 - Is it safe to say that "Nic na tebe nehledám" would essentially mean, "I am not looking/searching for some dirt (as in bad information) on/about you"?
2 - Is it safe to say that "Nehledám (něco) pro tebe" could be used to convey the meaning that "I am looking/searching for something, but not on your behalf and/or not in order to give it to you when I find it"?
Thanks for your help!