The Historic Places Trust says it hopes the Timeball Station in Lyttelton, which is to be demolished for safety reasons, can be rebuilt.
The Category One listed building, which has stood on the hillside since 1876, was extensively damaged in the earthquake.
The trust's chief executive, Bruce Chapman, says it is now too dangerous to consider doing anything other than demolishing the building.
But he hopes it will be possible to recover the timeball mechanism itself, and the trust will look at options for reconstruction.
Mr Chapman says they would like to reconstruct at least part of the building to try and restore some of its historic significance and its significance to the local community.
He says dismantling the Timeball Station will be a dangerous task, because of its location and difficulties in accessing the site.