While we're on the topic, I might as well add the info given by Goddard in Songs That Saved Your Life:
"Besides the ill-omened Cilla Black cover ‘Work Is A Four-Letter Word’ and the last Morrissey/Marr original, ‘I Keep Mine Hidden’, a handful of unfinished demos were also committed to tape, including a cover of Elvis Presley’s ‘(Now And Then There’s) A Fool Such As I’.
‘There was an Elvis song with a little bit of lyric’ says Showbiz, ‘half a song maybe, a very bad run through and a few other rough ideas. I had the tapes for a couple of years until I gave them back to Johnny for security. If he had any sense he probably burned them.’ Marr also confirms the existence of ‘A Fool Such As I’: ‘It’s true that we did it, but I didn’t like the song very much.’
Elvis had recorded his version in 1958 as one of several stockpiled tracks to be released at regular intervals while he was serving in the US army. The song wasn’t a hit until the following year, reaching number one in the UK on 15th May 1959, the week before Morrissey was born, and remaining there for another month. This historic detail almost certainly influenced Morrissey’s decision to tackle ‘A Fool Such As I’. It’s just as likely he saw in its lyrics a chance to vocalise his most private feelings about Marr’s potential departure; from its opening apology of ‘Pardon me if I’m sentimental when we say goodbye, don’t be angry with me should I cry’, to the more profound admission, ‘You taught me how to love, and now you say that we are through/I’m a fool, but I’ll love you dear until the day I die.’ According to Showbiz, ‘A Fool Such As I’ never saw the light of day because an engineer accidentally wiped off the first verse."
And the quote by Morrissey from a 2016 interview with news.com.au where he acknowledges its existence (he's wrong of course, there are other Smiths songs/demos that haven't been released yet, A Matter Of Opinion is one of them):
Q: "To your knowledge is there anything enticing left in the Smiths’ vaults that could be housed on potential future reissues?"
M: "Only a cover of Elvis Presley’s A Fool Such As I. I don’t even have a copy of it, but I expect it will spring out one day ... when I’m on a life-support machine."