The two umbrella organisations, which both have a large number of members from the voluntary sector, have had disagreements in the past over issues such as the extent to which charities should be involved in the delivery of public services.
They plan to meet in the next few months to see whether it is possible for them to work more closely.
"We are having a joint meeting to discuss how we can better coordinate things - both on the policy side and the service provision side," said Nick Aldridge, director of strategy at Acevo.
Aldridge said an exact date had not yet been set for the meeting, but that the two organisations were working out an agenda for it.
The news coincides with an announcement made last week by Stuart Etherington, chief executive of the NCVO, that his organisation was developing a new "suite of leadership services" for voluntary sector chief executives and chairs.
The project is typical of the kind of work that has previously been dominated by Acevo.
Etherington said: "We are investing more heavily in leadership services for our members."
He said that the new services the NCVO intended to offer included initiatives such as mentoring programmes.
In response, Aldridge said: "We're pretty clear that our primary focus is chief executives. So we would hope that, in developing things for chief executives, the NCVO would coordinate and collaborate with us."