The 66-year-old songwriter opened up about her relationship with the music icon in her autobiography "A Little Thing Called Life", reported Entertainment Tonight.
"I was still a virgin when I met him. I think that is what added to the allure of me for him. Because he was a very territorial man. And a very jealous man.
"Elvis was not monogamous. He just wasn't monogamous. He had a tremendous capacity to love and he loved women and women loved him... I was happy to share him with his legions of fans and even understood sharing him occasionally to infidelity, but it didn't make it any easier," Thompson wrote.
"When I was six years old, sitting at the breakfast table, I (told my parents), 'I am going to marry Elvis Presley,'she said.
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The pair eventually split in 1976, eight months before Presley died of an overdose of prescription drugs that caused his heart to stop.
"I saw prescription medication on his nightstand and when I questioned, 'Have you been ill?.' He stammered and he didn't really have a good answer for it.
"I had never been around drug abuse or alcoholism, my parents didn't even keep alcohol in the house, not even beer. I was pretty green going in," she said.
"I didn't think that lifestyle would be conducive to family life. I had to make a decision. It was a tough one and I felt depleted once I left," she said.