The Doors - Riders On The Storm
I could see Elvis crooning that one… Maybe even cut some of the instrumental stuff so its “radio friendly” for E and his audience.
Happy to oblige:
j
Is there nothing the internet can’t do?
But, contrary to "cut some of the instrumental stuff so its “radio friendly” ", it actually added some of the rambling from The End,
Which surprisingly works!
The one Bruce Springsteen wrote for him, but became a hit for the Pointer Sisters instead - Fire. Robert Gordon’s version is probably closest to the way Elvis would have sounded.
Yeah, I’ve loved The King (at a distance) for years, and I just guessed that it was something he might record. And, whaddaya know, there it was. And I agree, I was startled at how well the snippet from The End worked - so to address the OP, that’s what I’ll pick.
j
Thanks for that. The Elvis impersonating is pretty good, but those drums were awful!
Good to know I wasn’t the only one who noticed that …
Wind of Change by Scorpions
“Name a song you would have liked to hear Elvis Presley record before he died”
How about a song he could have recorded after he died:
Now that I think about it, “Touch Me” would be more fitting for Elvis
Do they have to be songs from his lifetime? Because there are many more recent songs that would be very memorable with Elvis singing them. Tim Munchin’s pope song, for instance. Or Kanye West’s Gold Digger.
I would love to have seen him in 1976’s A Star is Born with Streisand. In fact, he was her first choice.
Supposedly David Bowie wrote Golden Years for Elvis and offered it to him (they were label-mates at RCA at the time) but Elvis declined.
Mentally I am currently hearing Elvis singing Nazareth’s Hair of the Dog with Scotty Moore on guitar.
Elvis cursing on stage? Never!
I still can’t imagine him singing “Hair of the Dog”, though 
Wild One (Real Wild Child). Kinda the Australian “Louie Louie” and covered by Jerry Lee Lewis, Iggy Pop, and a host of others. Would have been perfect for Elvis.
Now that I think about it, I would love to have heard Elvis sing the Prince song I Want to be Your Lover.
It would be kind of surreal to hear Elvis singing Richard Thompson’s “From Galway To Graceland”.
Highway to Hell. That way he’d have some hard rock cred. Maybe he could get Pat Boone to help him, Oh wait, Boone was metal, right?
Remake the Chipmunks Christmas song.
The Pharoah’s song from Joseph and the Amazing Technicolor Dreamcoat, which is written to be sung Elvis-style. IIRC, Elvis wanted to play the part, but someone (I don’t remember who) didn’t want him to.