Weir, however, said any terms of negotiation were commercially sensitive and the move was strictly temporary.
Parkin would not comment for this article.
Statistics New Zealand's building at CentrePort was damaged in the 7.8 magnitude earthquake to the extent that it could be up to a year before it can be reoccupied.
The Government, meanwhile, has launched an investigation into the failure of relatively new buildings - including Statistics House - following last week's quake.
Announcing the investigation, Building and Housing Minister Nick Smith said the earthquake had tested the seismic strength of many of Wellington's multi-storey buildings.
"This investigation will focus on Statistics House to understand its performance and where there may be wider lessons for improved design," Smith said.