The 'Marry The Night' singer, who is currently touring Europe in support of her latest album Born This Way, is said to have planned the construction of a guest nursery for when Sir Elton John and David Furnish's son comes to visit.
"GaGa is going to give Zachary his own nursery which includes a huge bedroom, playroom and bathroom [which] will overlook the Cretan sea," a source told the paper.
"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."
The 26-year-old singer was first seen visiting the Greek island with ex-boyfriend Luc Carl in October 2010. She is reportedly very close to her godson, and is said to have given him a personalised story book on his first birthday earlier this year.
GaGa recently revealed that her new album is called ARTPOP and teased possible lyrics from the record on her Little Monsters social network.
Watch the video for Lady GaGa's 'Marry The Night' below: