The finding emerged in a survey carried out by market research firm iCD Research. It comes as the organising committee, Locog, attempts to tie up sponsorship deals with a raft of companies in six categories including telecoms, insurance, automotive and utilities.
Some of the names that have been touted as potential sponsors over recent months include HSBC, Citibank and Bank of America in the financial category, and BP from the oil and gas sector.
However, according to the report, the majority of people surveyed believe companies such as BP should not be allowed to sponsor the Olympics if the organisers' 'green and sustainable' selection criteria are to be met.
The survey, which sampled 1,000 people, found that 67% rejected oil and gas as a category the organisers should seek to partner.
Other unpopular categories included automotive which polled 57% in the negative. Telecoms was rejected by just 11%.
Citibank and Bank of America received a lukewarm response as potential sponsors, with 50% of the public claiming they did not welcome sponsorship by overseas-owned companies.
Paul Dixon, managing director at iCD Research, said: "Locog and the Government have a lot of work to do to convince the public and sponsors that the Games are good value for money.
"Locog has also shot itself in the foot by claiming that sponsors will have to meet green and sustainability criteria, when the public are clearly sceptical about the track record of a number of industries being courted."
The results of the survey coincide with a damning report by British members of Parliament, which raises questions about the spiralling costs of the London 2012 Olympics.
The report said figures in the budget were "seriously outdated" and gave doubts to claims the Games would achieve a lasting benefit.
Olympic minister Tessa Jowell has already admitted the budget for building the infrastructure for the Games had been undervalued.
If you have an opinion on this or any other issue raised on Brand Republic, join the debate in the Forum.