CfBT Education Trust refused to say why it had not bid to run the Fast Track scheme beyond August next year, when its contract expires. The scheme was launched in 2001 and now receives around pound;12.5 million a year funding.
Fast Track was criticised recently by Barry Sheerman, the chairman of the Commons select committe that covers education, who said plans to restructure it next summer removed its best elements, including its residential courses.
Teachers have also criticised the project recently, saying they lacked support from tutors and received "banal" advice.
Alex Brassey, a London teacher who has been on the scheme for several years, said the project seemed on its last legs. He said: "In the past year I've noticed they have been contacting me a lot less, I get less material through the post and less contact with my tutor."
Fast Track's total budget since its launch has been pound;76.93million, or pound;469,000 for each of the 164 "graduates" who have so far progressed to senior roles.
There are 1,900 teachers still on the scheme, although some perks, including free laptops for trainees, have been axed.
The National College for School Leadership has overseen Fast Track since 2006 and will award the three-year contract. It was unable to name the bidders.
CfBT runs a handful of government programmes including the Gifted and Talented programme, and has an annual turnover of pound;100 million and 2,000 staff.
Margaret Abbott, UK services director at CfBT said it would work closely with NCSL and others to ensure there was "no disruption of service" to Fast Track teachers.
A consortium led by Lord Puttnam and Lord Bragg, which includes Channel 4, television producers Mentorn Media, and The Guardian, have joined the bidding for Teachers TV. Ten Alps, Sir Bob Geldof's production company, has the contract to run the government-funded television channel until August and will also be entering a renewed bid.