Bradley Cooper and Irina Shayk were 'on and off' for the past year, source says - CNN

The relationship has been strained, according to the source, over Cooper's "intense" work-ethic during production and press for "A Star Is Born."

"He's into bettering himself, and his career and doesn't want distractions," the source said. "When he does a role, he stays in character, at least partly, all during filming."

Cooper, 44 and Shayk, 33, have parted ways after being in a relationship for four years, a second source close to the couple told CNN.

But early in his time together with Shayk, Cooper spoke to friends about wanting to marry her.

"He said she was 'the one'" in 2015," the first source said, who added that the couple has been "on and off for about a year now," trying to work on things for the sake of their 2-year-old daughter.

Cooper and Shayk recently attended Jerry Seinfeld's 65th birthday party at New York's Cafe Carlyle in late April.

In February, Shayk had told Glamour UK she's not going to share her personal life with the public.

"I have a lot of friends who share a lot of their personal life on Instagram or social media, very publicly," she said. "I admire it and I think it's great -- but I think it's all about personal choice. Because my work requires me to be out there, I just decided my personal life will be quiet. That's why it's called personal, because it's something for you and your family, and I feel happy with it."

CNN has reached out to reps for both Cooper and Shayk for comment.

Cooper's "A Star Is Born" co-star, Lady Gaga, recently opened up about her split in February from her former fiancé, Christian Carino.

"Last time I sang this song, I had a ring on my finger, so it'll be different this time," Gaga reportedly said during a performance of her "Jazz and Piano" show in Las Vegas over the weekend, before singing "Someone to Watch Over Me."

Gaga and Cooper's show-stopping duet of "Shallow" at the Academy Awards earlier this year inspired fans to express speculation and hope on social media that two would make their on-screen romance real.

Lady Gaga and Bradley Cooper perform onstage during at the Oscars in February.

Gaga responded with a big eye roll to suggestions the two had a thing.

"First of all... social media, quite frankly, is the toilet of the internet and what it's done to pop culture is abysmal," Gaga said in an interview with Jimmy Kimmell days after the performance. "People saw love and, guess what, that's what we wanted to you to see. This is a love song."

Cooper directed their film and intended for them to appear close during their Oscar performance, she said.

"From a performance perspective, it was so important to both of us that we were connected the entire time," Gaga said. "I've had my arms wrapped around Tony Bennett for three years touring the world. When you're singing love songs, that's how you want people to feel."

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