Others believed there should be no prohibition and that the acceptance of funding should be left to individual moral judgements.
Professor Steve Weaver, the board's chairman, outlined the discussion in a university council meeting held last month.
According to minutes released this week, Professor Weaver said there was a diverse range of views and with no clear consensus a working group had been set-up.
One member proposed a case-by-case "blush test", and there was general support for academics' freedom to not accept funding for work they did not approve of.
Under current systems anything contentious can be referred to the research and innovation department for a decision. Nothing had been referred for the past four years at least, Professor Weaver told the council.
A spokesman for the university told the Weekend Herald that Professor Weaver was unwilling to answer questions on the ethical research funding discussion as it was ongoing.
The university council minutes do not elaborate on the possible reasons given in support of the proposal to reject research funding from dairying and other industries.
However, Canterbury's burgeoning dairy industry has led to concerns about water pollution and nutrient losses, with calls to limit dairy conversions. When academic advice on research funding has been received the University of Canterbury's finance committee will also discuss the parallel issue of ethical investment.
Professor Sally Casswell, a Massey University public health researcher with a particular focus on alcohol, said she strongly believed research funding should not be accepted from the alcohol industry.
Such funding was an attempt by the industry to position itself as a partner in policy research, Professor Casswell said, but only industry-friendly policies were supported.
"When universities take money, they are being co-opted into this scenario ... it gives [the alcohol industry] an aura of respectability."
However, Dr Eric Crampton, head of research at the NZ Initiative think-tank, said industry-funded research could be extremely valuable, so long as funding arrangements were disclosed and unethical behaviour could be censured.
Dr Crampton previously worked at the University of Canterbury's economics department and was frequently critical of research on the societal harm from alcohol.
He maintains an adjunct senior fellow position with the department.
One-fifth of his university position was funded through a grant from the Brewers Association of Australia and New Zealand, he said, "and everything that I did was totally up for anybody to look at or comment on, or censure me if I was behaving badly".
"It is distortionary to automatically believe that industry funding is bad and evil and that government money comes with no strings and no agenda."
