Hawke and Shawhughes, who married in 2008, have a 2-year-old daughter.
Hawke also has a son and daughter from his previous marriage to actress Uma Thurman. Shawhughes at one time worked as a nanny for Hawke's older children.
An insider told UsMagazine.com Shawhughes is "five months along, totally showing."
"They don't know the gender, but ... Clementine really wants a little brother!" the source said.