Bradley Cooper has a "huge and overwhelming connection" to Lady Gaga, but a romance is "premature," an entertainment source tells PEOPLE

Bradley Cooper‘s relationship with Lady Gagais one of a kind.

“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,” an entertainment source tells PEOPLE.

And while the pair's chemistry is strong and allowed their film A Star Is Bornto soar to great heights (see its eight Oscar nominations), the rumors of a possible romance between themmight have played a role in Cooper's split from ex-girlfriend Irina Shayk. Gaga and Cooper made headlines for their intimate Oscars duet of “Shallow,” which earned the singer an Oscar for Best Original Song.

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

Lady Gaga and Bradley Cooper Matteo Chinellato/NurPhoto/Getty Images
Lady Gaga and Bradley Cooper Matteo Chinellato/NurPhoto/Getty Images

PEOPLE confirmed last week Cooper and Shayk had called it quits after four years of dating. They share 2-year-old daughter Lea De Seine.

A different source had previously told PEOPLE that, before news of their split became public, Cooper and Shayk had “spent a lot of time apart.”

“[Irina is] not focused on the celebrity part, or on the fame — she just wants to protect her family,” the source shared. “Bradley is very into work and is trying to take advantage of every career opportunity right now.”

After awards season was over, a separate insider told PEOPLE in April that Cooper made spending time with their family a priority.

“After awards season ended, Cooper slowed down to focus on his family,” the insider said, sharing that the star spent “every day with his family.”