the idea is that "who" is used for a person, and "that" for an idea. in this specific situation, the "that" refers to lack of knowledge (of a thing) rather than of a person, but only a person can love her, so who ought to be used.
You could also say "There is no one of whom I am aware that would deserve to love her."
This is actually a pretty sticky grammatical discussion because of the supposedly unacceptable use of "I know of", and the general idea that the use of who/whom twice in one sentence is a potential source of confusion and might sound odd.
As written, the sentence says "I have no knowledge of anyone who deserves to love her." and would be better stated that way. The use of "there is no one" is the main problem. It is an indirect statement that forces odd structures later in the sentence, so is best avoided. An editor might just say "rewrite" or "awkward sentence".