'avid reader of' is correct and usable in written English.
You can use it to describe someone who enjoys reading a lot. For example: He is an avid reader of fantasy novels.
I am an avid reader of The New Yorker.
An obviously avid reader of our May 28th issue,.
He is an avid reader of Philip French's film criticism.
The Unabomber was an avid reader of Dostoevsky.
As an avid reader of honest-to-goodness books, I agree that tablets are extremely distracting.
I am an avid reader of your print newspaper and enthusiastically follow the newspaper industry.
Bougainville was an avid reader of the "Discourse on the Origin of Inequality".
She was an excellent photographer and an avid reader of Proust and other great literature.
Arthur was an international competitive backgammon player, painter, and avid reader of history.
It is an avid reader of The Huffington Post, Jihad Watch, Technorati and, oddly, TruckingInfo.com.
The Afghan president is an avid reader of the British press on his country.
