Teach First, which puts high-flying graduates into the classroom after just six weeks, has met with officials from Glasgow and East Ayrshire.
The organisation is also to hold meetings with the General Teaching Council for Scotland (GTCS) about operating north of the Border. However, it has been told the scheme it operates in England and Wales would not be permitted in Scotland.
Teach First, introduced under the Labour government in 2003, has been a central plank of the Coalition schools policy, with Michael Gove, the Westminster Education Secretary, promising to quadruple the number of recruits.
It sees graduates with degrees of 2:1 or better placed in schools with low exam results or large numbers of disadvantaged pupils after only six weeks' training.
However, the Educational Institute of Scotland (EIS), the country's largest teaching union, believes the scheme threatens the terms and conditions of qualified teachers and undermines quality.
Larry Flanagan, EIS general secretary, said: "We continue to oppose this type of approach, which places delivering education cheaply above guaranteeing quality education provision from a fully-qualified teacher workforce."
However, the GTCS said no-one could teach in a local authority in Scotland without being registered with it. The organisation does not register anyone without a degree and an appropriate teaching qualification.
A spokesman for the GTCS said: "We have been approached again by Teach First to meet and discuss its desire to work in Scotland and we will meet with Teach First as we would with any organisation seeking advice about teaching in this country."
A spokeswoman for Glasgow City Council said the meeting with Teach First was purely to clarify the way the Scottish system worked. She said: "We were approached by Teach First to discuss a specific model for Scotland and we told them they would have to develop a bespoke Scottish solution signed off by GTCS."
It is understood, however, that if a way could be found to use Teach First staff alongside teachers in line with GTCS rules that would be welcomed if it provided extra resources in deprived areas.
Graham Short, executive director of educational and social services at East Ayrshire Council, confirmed talks had been held but any agreement would need to be agreed by the GTCS.
He said: "Teach First has been involved in informal discussions with local authorities in Scotland, including ourselves. At the forefront of the discussions has been the shared aim of securing the best outcomes for children, particularly from disadvantaged backgrounds. However, the discussions have also emphasised the differences between the Scottish and English education systems. One of the key aspects of difference is the requirement for registration of teachers by the General Teaching Council for Scotland and this matter would require to be resolved at national level before any local use of Teach First, even in a pilot exercise, was possible."
James Westhead, Teach First's executive director for external relations, said: "We have had a number of conversations with Scottish local authorities, regulatory bodies and government officials, who have expressed interest in better understanding our work with schools in low-income communities in England and Wales. We are open to continuing these if there is interest.
"As a charity committed to ensuring all children receive the best possible education, our trainees receive the highest quality training and development. Our teachers receive more training than is required through other routes. All must achieve the gold-standard PGCE teaching qualification and Teach First enables all its teachers to go on to complete a highly-regarded masters qualification."
The EIS also re-affirmed its belief comprehensive schooling offered the best model of education for Scotland. Mr Flanagan said: "Michael Gove's drive in England and Wales to introduce so-called academies and free schools, which are out-with local authority control, runs contrary to principles of local democratic accountability and is incompatible with the notion of equal opportunity in state-funded education."