Estelle Morris this week refused to rule out a dramatic return to education when she quits Parliament next year.
The former education secretary is being tipped as a possible new chief executive of the Government's National College for School Leadership. The pound;149,033-a-year post will become vacant early next year, when Heather du Quesnay, stands down.
Ms Morris, the arts minister, has already announced she will resign at the next general election, but sources say she may quit early, forcing a by-election in her Birmingham Yardley seat, if the right job comes along.
Speaking to The TES, Ms Morris refused to dismiss speculation linking her to the college, but insisted she was considering a series of options. "I would not want to talk too much about that," she said. "That's not an evasive answer because I am still talking to a lot of people about what I might do.
"It's like when you are young, you want to consider every option before you make your mind up about what you want to do. You tend not to say 'no' to anything at this stage, and I have not yet decided what I want to do or whether that will involve anything to do with education again.
"But I have certainly not put in an application (to NCSL) or talked to anybody about it."
Ms Morris is due to give a lecture at the NCSL's conference centre next month, only the second time she has ever visited, and says she remains a big fan. "I think it is absolutely super," she said. "It is a beautiful building and a real sign of the importance now being attached to school leadership. It has gone through the 'setting itself up' phase and I think Heather du Quesnay has done a really good job. In its next stage, I think it will start to fly."
Other names linked with the position include leading civil servants Peter Housden, the Department for Education and Skills' director general of schools, Mike Gibbons, director of the DfES innovations unit, and Professor David Hopkins, director of the standards and effectiveness unit.
Mr Housden is the former chief executive and director of education of Nottinghamshire county council, close to NCSL's Nottingham university headquarters. Professor Hopkins is a former dean of the university's school of education, and Mr Gibbons is a founder member of NCSL's governing council.
Others in the frame include Pat Collarbone, director of leadership programmes at the college.
Unions have called for existing or recent headteachers to be given the job amid fears the college is being swamped by bureaucracy and losing focus.
Leading secondary heads with responsibility for more than one school are likely to be in the frame, including Sir Dexter Hutt, executive head of the Ninestiles federation of secondary schools in Birmingham.
Ms Morris was one of the early champions of the college when it was set up to lead the training of heads and senior teachers in 2000 following her appointment to the Cabinet in June 2001. She resigned in December 2002, a day before she was due to officially open NCSL's new pound;28 million conference centre.
John Dunford, general secretary of the Secondary Heads Association, who is understood to have applied for the job last time, ruled himself out this time.
"It was always my view that the college should be led by someone with recent successful headship experience," he said.