The 'Born This Way' hitmaker is having the wing built for Zachary Furnish-John in her new home on the Greek island of Crete, reported Sun online.
"GaGa is going to give Zachary his own nursery which includes a huge bedroom, playroom and bathroom and will overlook the Cretan sea.
"She's already flown in special wallpaper and a big boy bed for a toddler because she knows the place won't be finished for months," said a source.
Proud parents Elton John and David Furnish can't praise GaGa enough.
"She's all about inclusiveness and tolerance. She believes you can be whoever you want to be, we don't have to live in a world of conformity and we can all benefit from individuality," David has said.