In a report analysing the possible use of dormant assets, the umbrella organisation said it was important that the new body "does not displace existing and emerging funders and investors".
Mubeen Bhutta, policy officer at the NCVO, said: "It's a potentially very significant risk, but those involved are not unaware of that.
"It's very important that the new schemes should dovetail with existing funders. We are aware of funders' concerns about being displaced if they're not considered.
"Any new body should fill gaps, not replicate current organisations."
The report stressed that third sector organisations needed access to "the full range of funding options, including grants in aid, project funding, contracting and social investment".
The original consultation document for the bank, which was put forward by the Government-backed Commission on Unclaimed Assets in July, proposed that the new facility would provide grants, but focus on a new range of financial tools, including quasi-equity, lease financing, loans and bonds.
Bhutta added that local experts should be consulted on plans to use the money to help people in disadvantaged communities.
"The analysis of the purpose has been based on research undertaken by the Young Foundation, which makes a very compelling case," Bhutta said.
"But it's also important that there is full consultation with those working on the ground in the communities themselves."