The correct answer is: that I am reading
A subordinate clause ( a dependent clause ) begins with a subordinate conjunction (as, if, than, that, where, until etc) or a relative pronoun (that, who, whom etc.) and will have a subject and a verb. This clause can not stand alone as a sentence because it does not provide a complete thought.
that I am reading is a subordinate clause because it contains a relative pronoun that introduces it ( that ), a subject ( I ) and a verb ( am reading ). It can not stand on its own because it does not have any meaning.