The target companies, include GCB Bank, AngloGold Ashanti, and Ghana Oil Company.
Dr Sam Mensah, Chairman of the GSE Council, told an Annual General Meeting of members that the move could provide government about GH¢560 million to finance infrastructure development.
He said the letting go of government’s holdings is important to the growth and development of the Exchange.
Dr Mensah is also asking government to retain the exemption status granted capital gains in respect of listed securities instituted in 1990,but is set to expire by the end of the year.
Besides, the core capital market services such as the purchase and sale of shares should not attract tax under the newly value added tax on non-core financial services.
Dr Mensah also called for the extension of the three per cent tax rebate for the first three years for companies listing on the exchange to five years to encourage small and medium size enterprises to raise capital and list on the Exchange.
On the performance of the Exchange in 2014, Dr Mensah said profits jumped to more than GH¢4 million.
Volumes of shares traded there fell from 346 million shares to 207 million shares in 2014.