The Lord of The Rings actor plays Douglas as a young man in the film, which features Bryan Cranston as the blacklisted Hollywood screenwriter Dalton Trumbo.
Before taking on the part, Dean wrote to the veteran movie star to ask his advice, and he received a kind response from Kirk.
"I wrote him a letter," Dean tells the Los Angeles Times. "He was very nice. He said, 'Don't worry about being me too much, just play the role, play the scene.' I thought it was a great answer. I think it was Kirk Douglas' way of saying no one but me is me."
Director Jay has now revealed that Kirk has seen the finished film and was impressed with Dean's performance.
"He said the only guy who could have done better at playing Kirk than Dean was... Kirk himself," Jay adds. "Douglas said he was upset we didn't ask him!"
The moviemaker goes on to echo Kirk's praise of the performance: "Dean's interpretation of Mr. Douglas required more overlap of Dean's own heart and soul with the essence of Kirk Douglas. If Dean had tried to mimic Douglas, the iconic mask might have gone more opaque. What Dean did is much more like channelling Douglas through his own face and body."
Reports suggest the film's star, Bryan, took a preview copy of the movie to Kirk in person and even sat and watched it with him.
"Cranston brought the film to Kirk's house," a source tells New York Post gossip column Page Six. "They started at 3pm, took a break for dinner, then watched the rest. Kirk loved it. He gave Bryan a big hug."