The 30-year-old actor stars as the late King of Rock and Roll in the forthcoming Baz Luhrmann film, and admits he was "terrified' about performing as the 'Suspicious Minds' hitmaker, but Rami, who played Freddie Mercury in the 2018 biopic about the late Queen frontman, told him he would end up loving those days the most.
Sharing Rami's advice he gave him in a behind-the-scenes clip of 'Elvis', Austin said: "He said, 'You know what? Those days will probably end up becoming your favourite days.'
"He could not be more right about that ... I was terrified every time before going out there ... But Elvis said it as well. Those first couple songs, once you do them and you realise OK, nobody's going to throw a rock at me, it's all OK."
He added: "Then you feel that connection and you feel how you can play with the audience.
"There were days I didn't want the day to be over."
He managed to win over the Presley family and even his co-star Tom Hanks, who portrays Elvis' manager Colonel Tom Parker.
The 'Castaway' star gushed: "When he came out on stage he was electrifying!
"I think he had to do it 30 times, with everything that was going on, and you could not take your eyes off of him every single time.
"You just wanted to see him do it again and again and again and again.
"Part of that is certainly channelling, part of it is the drive that Austin has, and always has as an actor. But there's also a huge amount of faith that he had in the process and in himself that is not unlike Elvis."
Austin revealed he spent every waking hour "obsessing" over Elvis and swotting up before nailing his audition.
Asked how he prepared, he said: "I said, 'I'm just gonna drop everything and I'm gonna obsess. I'm going to allow myself to obsess.
"And so I just started reading and watching everything I could on his life and on his friends and on his relationships and listened to only his music."
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