The venue would undergo "significant" strengthening work in order to be put back to use.
The Museum Stand is identified as a category 2 historic place as part of the Basin Reserve historic area.
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Opened in 1925, the stand once housed the players' changing rooms and lunch facilities, but was later used for public seating and toilet facilities.
It has been closed to spectators since 2012 as it is at risk of catastrophic collapse in an earthquake.
Strengthening the stand could cost up to $8 million, while knocking it down and replacing it might cost about $800,000.
The New Zealand Cricket Museum sits below the stand.
Lester previously said he was in favour of demolishing the stand, saying "it's going to be a very expensive option to have it strengthened and restored and I'm not sure that can be achieved".
Basin Reserve Trust board member and city councillor Simon Woolf has also said increasing capacity on the grounds were a priority.
"It might look pleasing, but it's my personal opinion that the stand is not fit for purpose."