The 29-year-old "Born this Way" hitmaker, whose changing shape recently sparked speculation she is pregnant, got engaged to Kinney in February but they are unlikely to tie the knot until next year at the earliest, reported Heat magazine.
"It's much more important to her and Taylor to get busy building a family than having a ceremony. Gaga hasn't planned any specifics yet but she's telling friends that she and Taylor won't marry until at least 2016," a source said.
And the singer and her 33-year-old fiance are keen to have a large family together.