The couple, who have been together since past one year, are getting more serious about their relationship, reported E! online.
"Things are getting more serious between them. They have spoken about having a family soon and building a future together.
"Irina would like to have kids in the next few years. Being a mother is something that is very important to her...Things are moving in an amazing direction," a source said.
While the duo have been busy with their respective careers they do take out time for each other.
"Bradley is very supportive. Irina is doing so well in her career at the moment. She has been getting gigs left and right-the demand for her with new campaigns is insane. She has to turn down jobs at this point," the source said.
Cooper, 41, and Shayk, 30, were first linked in April 2015 after they were spotted attending Broadway's "Finding Neverland".
They made their red carpet debut together at the L'Oreal Red Obsession Party in Paris in March. Last month, the couple attended the Met Gala and were photographed at an after-party.
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