Cobb is the former personal assistant and longtime best friend of singer Jessica Simpson, who is expecting her second baby.
"Looks like @donald_faison and I are going to have a little stormtrooper of our own!" Cobb wrote Thursday in a caption for a photo of T-shirt depicting a baby-sized "Star Wars" stormtrooper, UsMagazine.com said.
The baby's gender and anticipated due date were not mentioned in the online message.
The couple married in December 2012.
Faison has four children from prior relationships.
NBC reportedly holds celebs hostage to Jimmy Fallon's show
Aaron Carter is still in love with Hilary Duff