The 30-year-old Russian model had showcased her baby bump while walking the runway at the 2016 Victoria's Secret Fashion Show last month and multiple sources told E! News she and Cooper, 41, were expecting their first child. The two have been dating for more than a year and a half.
The two have not commented on the pregnancy. A source told E! News exclusively Irina and Cooper know the sex of their child and are currently in the process of narrowing down the list of names for the baby.
"Irina and Bradley are so excited to be parents," a source told E! News exclusively. "They have already picked a few names they like. They know the sex but are still deciding between some names."
David M. Benett/Dave Benett/Getty Images For L'Oreal
And the two are even thinking about expanding their family even more.
"Bradley and Irina love each other so much and this is not gonna be the only kid—there will be a few more after this one," the source said, adding, "Both families are very happy."
Another source had told E! News earlier this month the two "see themselves spending their lives together and building a family with more than one child."
Last week, Shayk sparked speculation she and Cooper had gotten engaged when she stepped out wearing a large emerald ring surrounded by diamonds. The source did not specify whether Cooper proposed but told E! News an engagement and a wedding would be "very under the radar" for the couple.
Shayk is meanwhile continuing her modeling work.
"Irina is still working and doing shoots," the source told E! News. "She is feeling good eating what she wants but also is working out."
The other source had said earlier this month Shayk had been having some food cravings and was "exercising in moderation" even though she "is more tired than usual," adding that she had been traveling a lot and hadn't had time to see Bradley, although they did communicate several times a day.
The pair plans to spend the upcoming holidays together, the first source said. E! News learned earlier this month Shayk and Cooper planned on going on a tropical vacation over the holidays with their families and close friends.