Alec Reed, chairman of Reed Executive, and one of Labour's biggest cash donors, has been given a roving brief and is talking to teacher associations, local authorities and headteachers. It is understood he will report back personally to the Prime Minister's office.
Mr Blair wants to use private-sector expertise to solve one of the biggest problems in the public sector. This is despite last month's launch by the Teacher Training Agency of a #163;10 million recruitment drive, including a cinema advertising campaign in which celebrities name their favourite teacher.
It is believed that one of the most controversial options being considered by Mr Reed is increasing teachers' working hours - in return for more pay.
This week the Commons education select committee warned of an 11 per cent drop in the number of undergraduates studying teaching. In maths, one of six shortage subjects, applications have dropped by 36 per cent since 1993,and one-third of training places are unfilled. To make matters worse, almost one in four people taking postgraduate teaching courses does not go into the classroom.
Margaret Hodge, chair of the all-party committee, said: "We have grave concerns that if this crisis is not tackled, then the Government's drive to raise standards may not be realised." She said more had to be done than the TTA's latest recruitment campaign.
Mr Reed would not talk to The TES about his brief. But it is believed one of the most controversial proposals he is considering is to increase the statutory number of hours teachers work. Surveys by the School Teachers Review Body show teachers exceed the 1,265 hours laid down by law. Extending the working year would give teachers leverage for asking for more money on an increased-productivity deal. It could also lead to greater differentiation between the jobs of primary and secondary teachers.
All teacher unions have said that uncompetitive salaries are a major obstacle to recruitment. This is one of their major criticisms of the TTA's "No one forgets a good teacher" campaign.
Mr Reed is considering ways of attracting people from business into the classroom, for example by short-term secondments. He has also been discussing with teacher unions the pay and career structure of the profession, including the lack of progression, and the likely effect of the General Teaching Council.
Kathy Baker, the National Union of Teachers' principal secondary officer and one of those consulted by Mr Reed, told him: "We need a clear national strategy for attracting people into the profession. The problem of low morale must be addressed. Teachers should be the best advocates for the profession, but at the moment they are very demoralised. "
The NUT is working with the TTA to try to attract young people into the profession and has sent out questionnaires to sixth-formers and students of a similar age in further education.
Mr Reed, also professor of enterprise and innovation at Royal Holloway College, London University, last year gave #163;100,000 to Labour. He was one of seven leading businessmen who had never previously voted Labour who openly declared they would be backing Tony Blair.
Reed Executive is the holding company for Reed Personnel Services, which is the biggest UK-owned employment agency, and Reed Education Trust. Reed Personnel Services was this week awarded the contract in Hackney, east London, for its "New Deal" programme to get young and long-term unemployed people into jobs or education.