However, a particular story told by Sir Tom has made many believe perhaps The King also made a recording.
Speaking to Chris Evans on the BBC Radio 2 Breakfast show back in 2010, Sir Tom revealed: “I went on set and he [Elvis] was there filming and then he stops for a minute and is walking towards me, and I had a ballad out at the time called With These Hands and there comes Elvis Presley singing With These Hands walking towards me, it was like a dream, and I thought ‘My God, this is unbelievable’.
“When he got to me he said ‘how the hell do you sing like that?’ and I said ‘Well you’re partly to blame’.”
Sir Tom also told this story to Conan O’Brien, the US TV host, saying when Elvis walked towards him, he shook his own hands in Tom Jones-style, almost attempting to imitate the Welshman.