Graham Lane, education chairman of the Local Government Association, said councils would give up powers to plan sixth-form and other education for 16 to 19-year-olds.
Power would move to the Further Education Funding Council's regional committees, under the deal brokered between colleges and councils. In return, councils will get seats on the boards - and will appoint councillors to college governing bodies.
Councils are also offering to give college principals or governors at least one seat on local authority education committees under the proposals, hammered out during a series of meetings between the LGA, Association of Colleges and education minister Baroness Blackstone.
The new division of powers would come as part of a package to introduce a common funding formula for 16 to 19 education. The proposals, first revealed in The TES last month, will be unveiled at the AOC annual conference as part of a joint blueprint designed to end competition between schools and colleges.
Ministers want to stamp out what they believe are needless wars over student numbers, particularly 16 to 19-year-olds.
Planning could be organised over each FEFC region, but local authority leaders are considering using training and enterprise council boundaries as a basis for local partnerships.
Under the deal being considered, local authorities would retain some powers to run adult education. But Mr Lane floated the idea of local authorities becoming involved in direct FE funding, to help cope with local skills shortages. TECs would also be brought into a tripartite planning process.
Mr Lane said: "Local authorities are not out to run colleges. What we are interested in now is having a strategic role."
Both Mr Lane and LGA chairman Sir Jeremy Beecham will address next week's AOC conference at Harrogate to make their case for greater planning.
Mr Lane said: "The idea of me and Jeremy speaking at this conference represents a big change in thinking in local authorities. We are keen to say that the world of FE has been tremendously undervalued and it's very much part of the community.
"We are also looking at how FE might be funded by local government; if we are interested in producing, say, extra nursery nurses, it might be possible for us to get involved."
He said he was confident that the talks with ministers - said to be at an advanced stage - would solve problems of competition, and concerns over unequal funding of schools, sixth-form colleges and FE colleges.
The LGA's charm offensive comes as relations between colleges and their former council paymasters thaw. Many principals have called for greater co-operation within sixth-form and further education.
Mr Lane will also outline councils' proposals for reforming discretionary grants. Ministers are currently consulting on proposals to abolish the system and replace it with increased access funds for higher and further education.
Mr Lane said councils wanted to keep the power to award grants, but would concede guidelines to make the system consistent.
He said that authorities wanted to award maintenance grants to over-16s, but were considering plans to limit awards to fees for over 19s.