The council, which gets £10.4bn a year from government to fund adult education and training, is staging a conference jointly with Futurebuilders on 16 March.
The pair will urge not-for-profit organisations in London to develop consortia to deliver training.
The move comes as the council is suing one voluntary body that is delivering services on its behalf. The organisation being sued does not wish to be named because it fears for its future.
Stuart Etherington, chief executive of the NCVO, wrote to Alan Johnson, Secretary of State for Education and Skills, in January to ask whether the legal proceedings could be abandoned.
Etherington said in his letter that the council had breached the Compact on at least six occasions.
Janet Fleming, head of the Workforce Hub, said there was "a willingness to do things better" at the Learning and Skills Council. "There have been problems," she said. "What we have to do is watch and see whether new developments address them."
The council has arranged a meeting with the Compact Commissioner to discuss the Compact. A spokeswoman for the council said it was considering new procurement processes to create a level playing field for service providers.
Richard Gutch, chief executive of Futurebuilders England, said: "We have already invested in a number of consortia to support the delivery of public services, and we hope this conference helps many more come forward for funding and advice."