Kevin Curley, chief executive of the local umbrella body Navca, is backing Ed Miliband in the Labour Party leadership contest, the results of which will be announced this weekend.
"Of the five candidates, he has had most to say about our sector," Curley said. "He obviously understands it as he was the first Minister for the Third Sector. For this reason, he appeals most to me."
Other sector leaders were unwilling to back particular candidates, preferring to talk in general terms about the policies they would like to see the winner adopt.
Peter Kyle, deputy chief executive of the chief executives body Aveco, said: "We'll be looking for a clear commitment to developing the role of charities in supporting vulnerable people and delivering public services. Any candidate that discriminates against one sector as a provider should be treated with suspicion."
One leadership contender, Andy Burnham, said when he was health secretary that the NHS should be the preferred provider of health services.
Jay Kennedy, head of policy at the Directory of Social Change, said the election of a new leader would give the Labour Party the chance to rethink the relationship with the sector that it developed during its years in government.
"There should be a greater willingness to trust people, especially when the state provides money," he said. "The party should also devote policy space to the needs of local, grass-roots charities, rather than viewing charities primarily as vehicles to deliver public services."
He said the Labour Party had strong links with poverty and social justice charities in particular, and the new leader should attempt to build on those connections.
Curley added that getting the voluntary sector onside was more important for Labour than ever before: "With the big society, the Tories have taken on Labour in an area they have traditionally seen as theirs, and the sector is suddenly in the political mainstream."
Martin Brookes, chief executive of the think tank New Philanthropy Capital, said the new leader must respect the sector's independence. "They should do more to understand how private funding can create and support solutions to social problems," he said. "Private funding is not better than public funding, but it has a valuable role to play."
Ed Miliband probably has the most obvious link to the voluntary sector, having been the first Minister for the Third Sector when the Office for the Third Sector was set up in 2006.
But the other prospective leaders are also keen to highlight their charity links and credentials. For example, David Miliband's first job was as a parliamentary officer at the National Council for Voluntary Organisations between 1987 and 1988. Ed Balls says his role as children's secretary taught him the value of partnerships between charities and the public sector.