Johann Aguilera told Star magazine, "Christina's grandfather is 86 and her grandmother is 82. They have health issues."
"I don't know how much longer they're going to last. Time is running out."
Christina hasn't spoken to her father for many years, and that rift has extended to his brother and his parents.
Her uncle has urged her to make contact with her grandparents for the sake of her four-year-old son Max.
"I know how much joy it would give my parents if she came back into our lives again," Johann said.
"It would mean the world to them if they could see Christina before they die."