Mr Smith, head of St Peter's School, Northampton, has been invited to discuss his blueprint for a a voluntary GTC with a permanent secretariat liaising with the DFE.
Mr Smith's model would also have a code of conduct backed by disciplinary action for those who contravened it. It shares many features with a rival scheme which has already gained influential backing.
In contrast to Mr Smith's blueprint, however, those behind the rival scheme believe a GTC can only work if it has statutory backing which would transfer to it legal responsibility for advising on teacher training and professional development, as well as powers to dismiss or discipline teachers.
Hopes of gaining ministerial approval for a teaching council rose earlier this year when John Tomlinson, professor of education at Warwick University and chairman of the rival GTC (England and Wales), met the then education minister Baroness Blatch for talks.
Professor Tomlinson's committee has been operating as a voluntary teaching council since 1989, but believes a credible and effective council would require statutory backing and legislation to bring it into effect.
While the backers of the two schemes are divided over the precise status of a GTC both agree on the need for it and are prepared to work together. "All of the things the Government has done - teacher assessment, curriculum assessment - have been top-down. It has done nothing to encourage teachers to take responsibility for their own standards and training," Professor Tomlinson said.
Mrs Shephard has told Mr Smith that it is up to teachers to set up their own professional body to promote standards of conduct and good practice in teaching. But in a letter to him, she added: "I would certainly be prepared to consider how I could support such an initiative that seemed likely to be effective."
Mr Smith envisages the GTC would have a Royal president and has mooted as trustees Sir Rhodes Boyson, Baroness Warnock, Max Morris, Lord Glenamara and Ivor Sutherland, registrar of the Scottish GTC. There would be a nine-member executive council and a 50-strong general council: six seats from the trade unions, six from the Government, 18 from teacher organisations and 20 teachers who would be elected.
Influential backing for a GTC has come from the Commons Select Committee on Education, the Interim Advisory Committee on Teachers' Pay and the National Commission on Education. Both Labour and the Liberal Democrats have pledged to introduce the necessary legislation if they win the next general election.
The Government has in the past rejected calls to create a statutuory GTC, fearing it would be dominated by the unions. But Mrs Shephard has expressed interest in the scheme as a way of restoring teachers' morale and professionalism.