The annual ceremony, now in its 23rd year, celebrates "the most egregious passage of sexual description in a work of fiction".
The former Smiths frontman has been nominated for his first novel, List of the Lost.
It includes a reference to "one giggling snowball of full-figured copulation" and a "bulbous salutation".
Other books nominated so far include Erica Jong's Fear of Dying, which includes the passage: "You raised the kundalini... like an electric snake in your spine", and celebrated screenwriter George Pelecanos' The Martini Shot.
Michael Ashcroft and Isabel Oakeshott's Call Me Dave, an unauthorised biography of Prime Minister David Cameron, was brought to the judges' attention because of an allegation, by an unnamed source, about an initiation ceremony in which Mr Cameron is said to have taken part.
However, the Review said: "That assertion was so flimsily corroborated as to resemble fiction but, regrettably, the biographers displayed insufficient literary brio to merit serious consideration."
The purpose of the prize is "to draw attention to poorly written, perfunctory or redundant passages of sexual description in modern fiction, and to discourage them".
It does not cover pornographic or expressly erotic literature.
Last year's prize went to Booker Prize winner Ben Okri for The Age of Magic.
The winning content read: "When his hand brushed her nipple it tripped a switch and she came alight. He touched her belly and his hand seemed to burn through her.
"He lavished on her body indirect touches and bitter-sweet sensations flooded her brain."
Other winners of the prize include Melvyn Bragg, Norman Mailer and AA Gill.
This year's award will be announced at the aptly named In and Out Club, in London.
Morrissey is the favourite to win Literary Review's 2015 Bad Sex in Fiction Award.