In return, schools "lending" staff may be asked to take additional probationers for their induction training, paid for by the Executive. But schools would not be obliged to accept them.
The proposals form part of a variety of strategies discussed this week at a national seminar in Dunblane on managing student teacher placements - with a claim this week that only 30 per cent of schools make themselves available.
In next week's TES Scotland, Douglas Weir, former dean of education at Strathclyde University, will outline his own proposals, including the controversial suggestion of designating some schools as specialist training centres. This might be one answer to the current problem of finding suitable placements for all students.
The Dunblane seminar - attended by around 130 delegates from teacher education institutions, local authorities, the Scottish Executive Education Department and teacher associations - was the second national summit on the issue.
Concerns have been raised over the past year as training intakes have risen dramatically and more probationers have a guaranteed one-year induction.
Both schools and TEIs have argued that the ad hoc system of arranging placements has come under strain, prompting the Executive to fund authorities to appoint co-ordinators to ease the difficulties.
Christine Pollock, depute director of education in North Lanarkshire, believes that "significant progress" is now being made. She told the seminar that from next session the west of Scotland consortium of authorities served by Glasgow, Strathclyde and Paisley universities had agreed that the initial contact should be between the TEI and the co-ordinator.
"In the past, the local authorities were really out of the loop as the TEIs tried to maintain the very good relations many of them had directly with schools," Mrs Pollock said. "So the authorities did not know which of their schools were being used for student placements, and which were not. The appointment of co-ordinators now allows us to have an overview."
Another proposal accepted at the meeting was that TEIs should harmonise their placements so that schools did not have students arriving from different universities at different times.
Next year could see as many as 3,133 probationers looking for induction placements and 3,350 students on training placements.
Referring to the secondment of unpromoted teachers to TEIs, Hirek Kwiatkowski, dean of education at Glasgow University, said there was a will among authorities and the universities to make it happen.
"We would get the benefit of our departments being refreshed by experienced teachers - not heads of department - and the local authorities take the view that staff coming into TEIs would receive staff development which they could take back to schools," Dr Kwiatkowski said.
Bill McGregor, general secretary of the Headteachers' Association of Scotland, said the proposals were a "good principle" but not practical in the light of teacher shortages and difficulties in finding supply cover.
On student placements, Mr McGregor agreed that arranging local authority co-ordinators according to the three TEI consortia that have emerged - west of Scotland; Dundee, Edinburgh and Stirling; and Aberdeen - would be more effective. He acknowledged the need for a more structured approach, saying that 70 per cent of schools did not currently accept student placements.