The Commission for the Compact is unlikely to be given statutory powers during the current parliamentary year.
Labour MP Tom Levitt will next week present to Parliament a 10-minute rule bill calling for the commission to be given the powers.
But Levitt, chair of the All-Party Parliamentary Group on the Community and Voluntary Sector, told Third Sector there was little prospect of legislation being introduced before the summer recess on 21 July. "Success this year is a challenge," he said.
Ten-minute rule bills, which allow MPs to talk for 10 minutes, are primarily an awareness-raising measure.
Some MPs hoped the Local Democracy, Economic Development and Construction Bill, which had its third reading in the Lords last month, could be amended to include statutory powers for the commission.
But Sir Bert Massie, Commissioner for the Compact, said last month this would not happen and the commission would "look for future opportunities".
Richard Corden, chief executive of the commission, said Levitt's bill would put the Compact "on MPs' radars".
The commission was among 15 organisations to attend the first Compact 'refresh panel' meeting last week. The panel will discuss updating the agreement, which sets out how voluntary and public sector organisations should treat each other, by November.