Usually native speakers would prefer the phrase:
I'm reading a novel by Steinbeck
by denotes authorship, of and the possessive apostrophe are instead associated with ownership. Compare: "I'm reading a book of my father" which is ambiguous without previous or further context. (1) The book might be about my father; (2) he could be the owner of the said book, (3) he is the writer. Whereas "I'm reading a book by my father" means my father is the author of that book. In the case of "Steinbeck", the following phrases are grammatically correct:
I'm reading a book of Steinbeck
I'm reading a book of Steinbeck's
I'm reading Steinbeck's novel
the problem of ambiguity is unlikely because he is such a well-known author.
Oxford Dictionaries say:
3. Indicating an association between two entities, typically one of
belonging, in which the first is the head of the phrase and the second
is something associated with it:
the son of a friend
the government of India
a photograph of the bride [WITH A POSSESSIVE]: a former colleague of John’s
3.1. Expressing the relationship between an author, artist, or composer and their works collectively:
the plays of Shakespeare
the paintings of Rembrandt
Macmillan Dictionary says
4. used for saying who something belongs to
the property of the residents
They ended up living in the house of Jeanne's oldest brother.
5.concerning or showing someone or something
She had a photograph of him beside her bed.
It was a tale of war and bravery.
a history of Russia
16.used for saying who wrote a book or play, produced a work of art etc
the wonderful paintings of Picasso the plays of Harold Pinter