There are concerns that the voice of British investors has been muted due to increased international ownership of shares in UK-listed companies.
There are also worries about an excessively short-term mindset at UK companies.
This has been blamed in part for the banking crisis with powerful chief executives facing insufficient challenge from company owners.
The two organisations said: "The final stages of the discussion are still ongoing, and will result in the creation of an organisation, with a new name and a new chairman, that covers the full spectrum of investment management activity with a single, stronger and more coherent voice.
"The ABI will continue to represent insurers as asset owners."
There have been several attempts by policymakers to make companies more accountable to shareholders, including more binding votes on pay.
The European Commission published proposals earlier this week which included forcing executives to seek shareholder approval for their salaries and to justify the pay gap between management and their workers.
The ABI currently uses a colour-coded system to advise its members, with "red top" alerts highlighting the most serious concerns.
Between them, the two bodies manage trillions of pounds of assets.