It seems this is just a question for the ladies of the forum.
I cant imagine Elvis would have wanted to sing 'Always on my mind' to another man.
Good question Sophie but maybe it should have been 'Name 3 songs you'd like Elvis to sing'.
So let's see.
It would have to be 3 songs Elvis hasnt recorded so.
1. C,mon Everybody (made famous by Eddie Cochran) 50's vocals.
2. Sukiyaki with English lyrics written for Elvis (Made famous by Kyu Sakamoto) early 60's vocals.
3. Feelings (Made famous by Morris Albert) 70's vocals.