Graham Holley, the agency's new chief executive, said it needed to focus instead on attracting people to shortage secondary subjects, such as science and maths. "We don't think there is a need so much for an expensive campaign for primary teachers or for many of the other secondary subjects,"
The number of students allowed to do teacher training is expected to be reduced over the next decade as pupil numbers decline.
Mr Holley said that one of the agency's challenges would be to take advantage of this fall in numbers to raise the quality of staff joining the profession.
"Even if we did nothing the quality would improve as the teacher-training providers will be able to be more selective about the candidates they choose, but we need to go further," he said.
Mr Holley, 52, began working for the Department for Education and Skills as a civil servant when he was 19, believing it would just be a short-term job before he went to university.
Instead he stayed on at the department for most of the next three decades.
One of his most important assignments came in 1999 when David Blunkett, then education secretary, asked him to carry out a in-depth review of the Teacher Training Agency and make recommendations to turn round the decline in applicants for teaching courses.
As deputy director of the DfES's school workforce unit, he was then in charge of overseeing the five-year restructuring of the TTA, which later became the TDA. Mr Holley said these experiences have given him a unique perspective of the agency, where he has been acting chief executive since his predecessor Ralph Tabberer stepped down in March.
"I'm still hoping to go to university, but I'm going to have to wait until I retire," he said.
A study published last week by Education Data Surveys based on job vacancies indicated that too many teachers were being trained in subjects including history, geography and art but that there were too few in physics, chemistry and mathematics.