The report, In Work, Better Off, invites charities to bid against public and private sector providers to deliver employment training services.
Karin Pappenheim, chief executive of Employment Opportunities, a charity that helps people with disabilities to find employment, said many charities did not have the capacity to deliver large service contracts.
"In the big procurement programmes, more and more is being given out to private sector companies," she said.
Catherine A'Bear, chief officer of corporate affairs at the Shaw Trust, was disappointed that the green paper had "underplayed" the sector's key role in delivering existing New Deal contracts.
A spokeswoman for the Department of Work and Pensions said there were no plans to transfer decision-making about benefit sanctions from Jobcentre Plus.