The agency will be looking for something "distinctive" from new consortia wanting to offer training - such as courses that could attract ethnic-minority students, or plug gaps in schools in particular subjects or areas.
On-the-job training was championed by former chief inspector Chris Woodhead. However, though it has increased the involvement of schools it has not added to the overall quality of training, the agency said.
That view was angrily dismissed as "disgraceful" by the National School-based Initial Teacher Training Council. It insisted that the wrong measures were being used and such training produced better teachers.
Terry Creissen, the council's chairman, claimed the agency was discouraging school-based training.
He said his members had "raised the game for all training providers... There are poor providers in higher education but they don't get noticed so much. Our grades are going up."
But Nigel Vivian, the agency's head of quality ssurance, denied it was against school-based schemes. Some had proved very successful, he said.
He said: "We want to make sure that new providers are not competing with others for the same group of trainees."
Training in schools was introduced in 1993 by the then Conservative government. Groups of schools were allowed to operate as mini-training colleges, running courses and recruiting trainees to learn on the job.
They were endorsed by Labour ministers and championed by Mr Woodhead as a way of challenging "progressive" universities.
The former chief inspector was directly involved in setting up the first primary school-based scheme. However, despite some successes, Office for Standards in Education reports on such schemes have often proved critical.
There are around 50 school-based consortia, supplying 5 per cent of newly qualified teachers.
The agency said that, in future, it wants to accredit trainers offering something distinctive. It will also be more proactive in asking providers to bid to run new courses.
Consultations on how the TTA accredits training providers close on July 5. See www.canteach.gov.uk for more information or phone Tim Hickson on 020 7925 3817