The 57-year-old Australian actor stars alongside Kate Hudson in the biographical musical film - named after Diamond's 1972 song of the same name - about Mike and Claire Sardina's Neil Diamond tribute band Lightning and Thunder.
Jackman was thrilled to receive a call from Diamond, 84, telling him how much he loved the movie, and the pair then met up and sang karaoke together.
"Neil rang me crying because he was so moved by the movie," Jackman said during an appearance on The Graham Norton Show.
"I went to meet him and actually stayed the night. It was so great, when at dinner time, he suggested karaoke.
"We sang, I Dreamed a Dream from Les Mis, Can't Help Falling in Love, and Sweet Caroline. It was wonderful."
Song Sung Blue centres on two struggling musicians – Mike (Jackman) and Claire (Hudson) - who form a tribute act and unexpectedly fall in love.
Jackman acknowledged that stepping into the role of a performer impersonating another performer was a unique challenge in itself.
"It was confusing, but I had to sort of lose myself as a performer to become Mike and for Mike to become Neil. It was awesome," he said.
Hudson - who was also a guest on The Graham Norton Show - said she grew up near Diamond's home had never met him so asked if she could visit.
"It was such a lovely emotional meeting. He loves Mike and Claire and he loves the movie. He was so grateful for it which I was not expecting," Hudson said.
Jackman rose to global fame as Wolverine, portraying the Marvel superhero across 10 films from X-Men (2000) to Deadpool and Wolverine (2024).
While he's now focused on new creative projects, Jackman hasn't closed the door on returning to the role that earned him a Guinness World Record for the longest career as a live-action Marvel character.
"Maybe. I'm never saying 'never' ever again. I did mean it until the day I changed my mind," he said.
"I did mean it for quite a few years. I have done ten films now, so I think they have enough for an AI version of me."
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