They are among 17 potential sponsors for the academies. Others include O2, Microsoft and British Telecom. Channel 4 is supporting an application by Manchester Metropolitan university and Manchester College of Arts and Technology.
The BBC said it had been invited to apply by the council and believed that sponsoring an academy would be a good way to develop talent. More than 1,500 staff in London are to move to the corporation's offices in Manchester by 2010, where programmes such as University Challenge and Mastermind are produced.
"There is growth in the media sector in the city and, as we are a major employer and always keen to encourage new talent, we decided it would be a good thing to get involved," the spokeswoman said. "The BBC already does a lot of outreach work with community groups and this is the next step."
Usually academy sponsors give up to pound;2 million in exchange for control over key areas, such as ethos and the appointment of governors. The BBC spokeswoman explained: "We are not proposing to provide financial support but are exploring ways to use the skills and expertise of the BBC and its staff to inspire young people."
Judy Harrington, the vice chair of the Campaign for State Education, said the BBC's involvement in academies created a potential conflict of interest. "We are completely opposed to handing over control of schools to TV companies with no background in education."
Chris Keates, the general secretary of the NASUWT, said: "The issue is: should any company or corporation be able to own, govern and manage a state school? NASUWT would say no."
Manchester council plans to replace five schools with academies: Plant Hill in Higher Blackley, Brookway and Parklands schools in Wythenshawe, North Manchester high school for girls, in Moston, and North Manchester high school for boys, in Blackley. Aanother academy is planned for the east of the city. The total cost runs to pound;152m.
Pauline Newman, the council's director of children's services, said: "We are very pleased at the level of interest from companies within Manchester's economic growth sectors."
Other potential sponsors are the airport, an NHS trust, the Laing O'Rourke construction firm and the management consultancy Accenture. The council will hear a progress report on November 22.