Cooper was dressed in a red track jacket, jeans and Nike sneakers - a far more covered- up look than what Shayk, 33, was wearing in her most recent Instagram snap.
"The rumours about Bradley and Gaga having a love affair didn't help especially with his constant travels [promoting the film]", another People source revealed yesterday. "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 hard to speculate at this sensitive time".
"Since Bradley and Irina have always been very private about their relationship few knew there was really for sure something going on", the source said.
Gaga and Cooper co-starred in A Star Is Born a year ago and sparked romance speculation thanks to their noticeable chemistry, which was on display during their performance of "Shallow" at the Oscars in February.
She told Jimmy Kimmel: "People saw love and guess what?"
However, the rumor mill began to churn again as claims emerged that Bradley was "emotionally absent" from Irina as he was working on the critically acclaimed movie.
The actor was distant "during the long time filming" the musical drama with Lady Gaga, a source told People on Monday. Every women is sexy in her own way.
"They haven't been getting along for quite some time and seemed to be holding on to their relationship for the sake of their daughter", the source said of the couple's 2-year-old daughter, Lea.
A Star Is Born was Bradley's directorial debut; the film went on to get nominated eight times at the Academy Awards. I remember saying, "Well, I don't see it that way but there's also gay people in the world". She told W magazine, "They are actually the ones who discovered me, in Moscow".
The talent agent, 50, liked Shayk's Instagram photo of herself posing in front of a waterfall while on a photo shoot in Iceland, which she shared on social media Monday.
Lady Gaga's ex-fiancé Christian Carino approves of Irina Shayk's latest adventure.
PEOPLE confirmed the two had gone their separate ways in February after fans noted Gaga was not wearing her engagement ring at the Grammy Awards earlier that month.