The trams — decommissioned in the 1950s — have been in storage in Dunedin and it is intended one will be fully restored by the Tramway Historical Society in Christchurch.
The other could be salvaged for parts for other restoration projects.
It has been recommended the museum board, at a meeting this week, endorse director Cam McCracken’s decision to "de-accession" the two items.
Ownership of both could be transferred to the tramways society.
Takapuna DCCT No 66 was built in Auckland in 1923, bought by the Dunedin City Corporation Tramways (DCCT) in about 1928 and pressed into service as an electric tramcar in Dunedin in 1930, a report for the meeting said.
It was withdrawn from service in 1956, when the DCCT tramway system closed, and then reportedly spent the next 38 years as a crib in Harwood on Otago Peninsula, before being acquired by the museum.
It was transported there in 1994 and it was intended the tram would be restored, but a fundraising campaign did not generate sufficient support.
The historical society, which in 2000 assessed the car as "worth preserving at all costs, as it is the only remaining example of one of the most generally used tramcar types in New Zealand", proposes to fully restore it.
"The objective hoped for when the body was first rescued in 1994 will finally be realised," museum curator Peter Read said.
Also possibly headed for the historical society are elements of the Sydney bogie No 52 tramcar. Built in Sydney, Australia, it was part of a fleet that entered service in Dunedin in 1921 and 1922.
The double-truck cars, with eight wheels rather than four, became the mainstay of the Normanby, Andersons Bay and St Clair routes until the demise of the Dunedin tramway system in the 1950s, Mr Read said.
The No 52 car ended up in a field in Green Island until it was recovered in 1995 and given to the museum.
It was assessed by the Tramway Historical Society in 2000 as significant but "virtually beyond restoration" and only worth retaining "for its componentry and as a pattern".
The society asked to be given the option of completing a detailed survey, including photographs, "of the body and how it was constructed and perhaps to collect some of the internal components".
The report for the meeting said that the Sydney bogie could now "contribute to the future restoration of other trams". It also said Toitū did not have the funding required to restore the Takapuna DCCT No 66 tram and the museum lacked the in-house specialist skills or time needed for the restoration task.
Even if restoration were viable for the museum, Toitū did not have the space to include the tram in its existing displays, the report said.
"It is worth noting the museum already has two other smaller restored Dunedin trams in its collection, both of which are on display."