Bradley Cooper and Lady Gaga Romance Rumors 'Didn't Help' His Relationship to Ex Irina Shayk

A Star Is Born was a massive success for Bradley Cooper but the Oscar-winning film, co-starring Lady Gaga, may have contributed to his split from Irina Shayk.

As Cooper, 44, and Lady Gaga, 33, made headlines around the world with their film, a source tells PEOPLE the rumors of a possible romance between them exacerbated the rift between Cooper and Shayk, 33.

“The rumors about Bradley and Gaga having a love affair didn’t help especially with his constant travels [promoting the film],” says the source.

The insider adds, “He has a huge and overwhelming connection to Gaga but whether it becomes a real love story in their lives for all the world to see is premature, and it’s difficult to speculate at this sensitive time.”

Lady Gaga and Cooper made headlines for their intimate Oscars duet of “Shallow,” which earned the singer an Oscar for Best Original Song.

Although Cooper and Shayk were having troubles, not many people knew, as they’ve always kept their romance out of the spotlight.

“Since Bradley and Irina have always been very private about their relationship few knew there was really for sure something going on,” the source added.

RELATED: Bradley Cooper and Irina Shayk’s Relationship ‘Changed’ After A Star Is Born, Says Source

PEOPLE confirmed on Thursday that the pair, who share 2-year-old daughter Lea De Seine, had split after four years of being together.

Cooper had a big year in 2018 with the release of A Star Is Born, which was nominated for eight Academy Awards and marked his directorial debut.

While attending the BAFTA awards earlier this year, where Cooper accepted the award for best original music, the actor and director thanked Shayk, who also made the trip across the pond, for “putting up with me” throughout the years-long creative process.

“Most of all I have to thank Irina, for putting up with me for all the music I was trying to make in our basement for a year,” he said. “Thank you very much. Thank you.”

RELATED: Bradley Cooper and Irina Shayk ‘Spent a Lot of Time Apart’ Before Split: He’s ‘Into His Work’

A source previously told PEOPLE that as awards season for A Star Is Born came to a close, Cooper made spending time with their family a priority.

“After awards season ended, Cooper slowed down to focus on his family, a source told PEOPLE in April 2019, sharing that the star spent “every day with his family.”