"The vice president and Mrs. Cheney are looking forward with eager anticipation to the arrival of their sixth grandchild," Dick Cheney spokeswoman Megan McGinn said. She could not confirm the due date for the baby.
The Washington Post reported in Wednesday editions that the baby is due in late spring. The newspaper said Mary Cheney, 37, and Heather Poe, 45, who have been together 15 years, are "ecstatic" about the new addition.
Mary Cheney's pregnancy follows on the heels of the birth of a fifth child to Elizabeth Cheney and husband Philip Perry. Elizabeth Cheney went on leave as deputy assistant secretary of state ahead of the July birth.
Mary Cheney is currently vice president for consumer advocacy at AOL, but has been an aide to her father, serving in his 2004 campaign alongside Elizabeth.
McGinn said she had no information on whether Mary Cheney and Poe, who moved from Colorado to Virginia a year ago to be closer to the rest of the Cheney family, will try to go somewhere to get married.
Virginia voters last month voted for a ban on same-sex marriage in the state. In the 2004 election season, Vice President Cheney said the issue of gay marriage should be left up to the states and "people ought to be free to enter into any kind of relationship they want to."
In an interview with FOX News in May, Mary Cheney, who earlier this year released a book about her life, said she thought a federal amendment defining marriage as a union between a man and a woman "is writing discrimination into the Constitution."
The Post quoted the source close to the family as saying the circumstances of Mary Cheney's pregnancy will remain private. In an interview with the Post six months ago, when asked if she and Poe wanted children, Cheney said that was a "conversation I think I should have with Heather first."
The Associated Press contributed to this report.