Tauranga's deputy mayor, Kelvin Clout, who initiated the referendum, said the initial results were closer than he anticipated.
"I wouldn't propose the museum to be totally off the table, but I do believe there should be significant changes to the current museum proposal."
Clout said although the referendum was non-binding the results will be given serious consideration by elected members.
The preliminary results will be released tomorrow, and final results will be collated and published on Thursday.
The council's final decision on a museum will be made on June 28 when the 2018-2028 Long Term Plan is adopted.
Clout said the referendum's online voting option was a New Zealand first.
"I believe this is the way of the future and will enhance our local government democracy and public engagement," he said.
Museum referendum progress results:
Do you support the Tauranga City Council including a museum in the 2018/2028 Long Term Plan?
No: 16,895
Yes: 11,524
In terms of location of the museum, do you support:
A. Cliff Road?
No: 14,980
Yes: 7528
B. Willow Street?
No: 14,131
Yes: 7300