John Sexton, who holds 50,000 F&P Appliances shares, said he had gathered the support of a small group of investors who also wanted a meeting.
"Hopefully we can round up some more [shareholders]," he said.
"I would like to know, before we make a decision, how other people feel, rather than make a decision on my own."
Turner, who has been in contact with Sexton, pointed out that the Papakura-based investor had a background in dairy farming and meetings were more common in the co-operative model used by Fonterra.
"In the end it's up to individual shareholders to decide what they might do," Turner said.
Sexton said listed companies could learn a lot from co-operatives on shareholder relations and consultation. Organising a shareholder meeting that did not involve the company was an option, he said.
Tony Holman, another shareholder, also wanted a meeting and said he did not accept the company's comments that it would be very unusual to have one.
"Never mind precedent, how about need?" said Holman, whose father worked for F&P Appliances.
"It's all very well to take our money - that's great, that's the idea - but they should also take notice of what we want."
Norman Morrell, another F&P Appliances shareholder who contacted the Business Herald, said it was difficult not knowing how other investors felt about the takeover.
The company has said retail investors make up roughly 30 per cent of its total shareholder base.
Qingdao-based Haier - one of the world's biggest whiteware makers - posted offer documents to shareholders last week and an independent report on the offer should be sent to investors by October 10.
F&P Appliances has advised shareholders to take no action and await the report, which will include an independent valuation of the firm.
The offer closes on November 6.
Australian fund manager Allan Gray, F&P Appliances' biggest shareholder after Haier, has already accepted the offer, giving the Chinese firm a 37.46 per cent interest in the New Zealand company.
The company's shares closed last week at $1.19.