The Local Authority Pension Funds Forum has commissioned research ahead of a final decision on what action to take.
Its motive is to protect the value of funds, on the assumption that companies that meet environmental regulations will prove better long-term investments than those that do not.
Research consultant Ebba Schmidt said: 'We would question companies on their policies and possibly seek board level meetings.
The forum was due to demonstrate its financial clout at BP's annual general meeting today.
It was planning to oppose the directors' pay package because it is not linked to the
energy company's health and safety performance.
The forum fears any repeat of the past two years' disastrous explosions and oil spills in the United States would damage the value of the 1.2% of BP owned by council funds.
Forum chairman Darrell Pulk (Lab) said: 'It is important the investors give the company a clear message - if safety culture is to be at the heart of the business going forward, then it must also be inherent in the board's remuneration policy.'