Cheney, 60, is out of intensive care at a Washington-area hospital, where he has been recuperating since early last month after having the mechanism placed in the chest and attached to the heart's main chamber to help pump blood.
"He is still in the hospital, but he's doing well," his daughter, Liz Cheney, said on "Fox News Sunday."
"He's out of the intensive care unit and hopefully will be home later this week."
She said her father, who has had five heart attacks, has several hunting and fly fishing dates scheduled for later his year, "so we're very hopeful" that he can resume an active lifestyle.
Cheney was hospitalized in June for discomfort from fluid buildup related to his heart condition.
Celebrity Families of 2014 [PHOTOS]