Fee-charging schools should also be allowed to join the Government's specialist schools programme, as part of a raft of recommendations by a body that helps the two sectors co-operate.
The Independent State School Partnership, a pound;1 million-a-year scheme, was set up by the Government in 1998, giving small grants to enable individual state and private schools to work together. A report by the partnership's forum, which governs the programme, said that the 314 projects funded to date had helped break down barriers between the sectors and benefited pupils and teachers.
However, it believes that it could build on its success by increasing the collaboration between the sectors.
It said that private headteachers should be able to become school improvement partners (SIPs). From September all state schools will be visited by a SIP, normally a serving or ex-head, who will spend five days a year working with them to improve standards.
But John Bangs, head of education at the National Union of Teachers, said:
"I find this an extraordinary proposal.
"I am sure independent heads have many qualities but I would query how much they know about schools full of children from deprived backgrounds."
The report also recommends that fee-charging schools be allowed to join the specialist scheme, which gives secondaries extra cash to promote a particular subject in the local area. It suggests private schools could use the funding to support partner state schools in subjects - such as maths, science and foreign languages - currently in decline in the maintained sector.
The forum also recommends that the budget for the partnership's programme, which has already risen to more than pound;2m in the next academic year, should be increased further.
Eric Wood, chairman of the forum and former chief education officer for Warwickshire council, said: "With a specialist school system, the development of academies and greater school autonomy, this is a moment when the barriers of prejudice between state and independent schools can be dismantled."
Jonathan Shephard, chairman of the Independent Schools Council, which represents the majority of private schools, welcomed the report's findings.
He said: "We are highly concerned by the dramatic decline in the take-up of language, sciences and mathematics nationally. We are delighted to put some of the greatest assets of the independent sector at the service of as wide a group of pupils as possible."