The Country icon released the song in 1974, before it received a famous 1992 cover by Whitney Houston for romantic thriller The Bodyguard.
Parton revealed that Elvis also wanted to record a version of her hit, but she turned him down over the money.
Writing in The Big Issue’s Letter To My Younger Self, she explained: “I’d been invited down to the studio to meet Elvis and be there when he sang my song. That was the most exciting thing that had ever happened to me. Who doesn’t love Elvis?
“But then Colonel (Tom Parker, Presley’s legendary manager) called me the afternoon before the session and said ‘You do know we have to have at least half the publishing on any song that Elvis records?’
“And I said ‘No, I did not know that’. He said ‘Well, it’s just a rule’. So I said ‘Well, it’s not my rule’.”
Parton added: “And I cried all night long, ’cause I was so disappointed. It wasn’t Elvis, I loved Elvis. And I’m sure he was as disappointed as I was because he had it all worked up and ready to go. I know he loved the song.”
Speaking about Presley’s wife of six years, Parton said: “Priscilla told me later that he sang that song to her when they were coming down the steps of the courthouse after they divorced. That really touched me and I thought ‘Oh well, I can only imagine’. But it wasn’t his fault.”
Parton went on to choose Presley as her “last conversation” if she could speak to anyone from history, in order to officially end the feud.
She explained: “I’d probably talk about I Will Always Love You and say ‘Hey, I bet you were as disappointed as I was about all that and I still dream about you singing that song’.
“Matter of fact, I even wrote a song called I Dreamed About Elvis Last Night and I had an Elvis soundalike sing it with me and we actually sing ‘I will always love you’ in it.
“And one day, I’m going to put that track out. So I think that I’d talk to Elvis, and just clear that up with him.”
Parton received widespread praise earlier this month after it was revealed that she had funded a COVID-19. The star was confirmed to have donated $1million (£753k) of her own money to aid research by the Vanderbilt University Medical Center since the start of the pandemic.
The research centre played a key role in the development of a vaccine from US biotechnology firm Moderna.
After Parton’s role in funding the vaccine was revealed, she said she was “a very proud girl”.
“When I donated the money to the COVID fund I just wanted it to do good and evidently, it is!” she said. “Let’s just hope we can find a cure real soon.”
She also recently reflected on securing a duet with Miley Cyrus on her latest album ‘A Holly Dolly Christmas’.