In Place-Based Social Investment: A Prospectus for Growing the Local Social Economy, the SIB proposes setting up a network of funds that are run by local voluntary sector organisations.
It will invest £2m in supporting two pilot funds in Liverpool and Northamptonshire.
The SIB says that locally run networks would be more able than national lenders to invest effectively in community organisations and would interact more effectively with local public funders such as councils and local enterprise partnerships. They would also be able to provide support to social sector organisations to help them understand repayable finance, develop business plans and grow their businesses.
The SIB said its vision for local impact funds would see them "draw together into one place an appropriate blend of national and local actors and interventions" that would together achieve more than the sum of their parts.
It said it hoped to see this type of fund set up for each city and county area, with about £10m available to lend. Each fund area should be aligned with one local enterprise partnership area, the SIB said.
The SIB said the funds were designed to work closely with local enterprise partnerships, which distribute EU funds, so that the money could become "part of the funding mix". And it said it hoped the local impact funds would be able to receive funds from local public bodies, local and national private investors and national social investors, including Big Society Capital.
"We are so serious about the value that local impact funds can bring that we are committing to invest up to £2m in two local impact funds this year," said Jonathan Jenkins, chief executive of the SIB, in his introduction to the report.