The proposal was put forward in a green paper for the voluntary sector, launched by party leader David Cameron in Kent yesterday.
The paper, which will go out for consultation across the sector, also proposes legally protecting lottery proceeds for use solely in the sector, allowing central government employees time off work to volunteer and making the Compact enforceable.
The proposed new office would be held to account by Parliament through a new civil society select committee and charged with increasing the involvement of the sector across all policy areas.
"We are inviting the sector to shape what we hope will be the agenda we pursue in government," said Greg Clark, shadow third sector minister. Policies shaped by the consultation will be used in the manifesto for the next general election, Clark said.