The 53-year-old children's television programme began broadcasting on CBBC from MediaCityUK in September but there is no date for the building of the garden by Thrower's successor Chris Collins.
"I am no longer the custodian of the garden at Shepherd's Bush," said Collins. "The whole of TV Centre is up for sale. I'm just waiting for the go-ahead to build a new Blue Peter garden. These are BBC decisions."
A BBC representative said: "We are currently finalising plans for the new Blue Peter garden, which will be located on the roof of the studio building at MediaCityUK."
He added "All items from the old garden such as the sunken garden and statues will be carefully stored until a new home can be found for them."
BBC Workplace, the BBC caretaking department, is now managing the dismantled, turfed-over garden site.
In store are statues of former pet dogs Petra and Mabel plus a time capsule due to be dug up in 2029 and a Thrower commemorative plaque.
Blue Peter presenter Helen Skelton said a second garden including statues of Blue Peter animals might be placed in a piazza on the Salford site, but the decision would be made by Peel Holdings, which owns the BBC site at Salford. The Italian sunken garden may be too heavy for the roof garden and might also go into the piazza.
Thrower designed the Shepherd's Bush garden in 1974 and presented from there until his death in 1987.