The bill, to be presented to Parliament next week, will contain provisions for a 'right to challenge'.
Speaking to Third Sector at the launch of a ResPublica report on community rights yesterday, Clark said the right to challenge would allow charities and community groups to bid to provide services if they thought they could do it "differently or better" than the groups the council had chosen.
"I don't want to give away the details of the bill, and it's legally complex," he said. "But it's all about community groups and the voluntary sector.
"If they can demonstrate that they can do things differently and better, councils should take that into account."
Asked whether the right to challenge would be given exclusively to not-for-profit groups, Clark said: "I wouldn't say exclusively. But the details will be in the legislation."
Some charities have previously raised concerns that the right to challenge would allow private firms to challenge councils' decisions by offering to provide services more cheaply than voluntary groups could.
The ResPublica report, To Buy, To Bid, To Build, said public assets, such as libraries, swimming pools and community centres, should be transferred to local community groups, rather than to the private sector.