The couple are apparently looking for a property that is suitable for bringing up children, reported Us magazine.
"They are definitely going to keep looking for new apartments in the city where they can raise a kid. They are New Yorkers and plan on being New York parents," a source said.
Dancy, 37, recently finished his 'Venus in Fur' Broadway run, and 33-year-old Danes just wrapped production on season two of American TV show 'Homeland'.
She was nominated for Outstanding Lead Actress in a Drama Series at the Primetime Emmy Awards 2012.
"Hugh and Claire decided a while back that they were going to have a child together. But they wanted to work their schedules around it," the source added.
The couple, who starred in the 2007 film "Evening" and married two years later, are enjoying every moment of her first pregnancy.
"Hugh is so excited to be a dad. They are going to be amazing parents," the source said.
