Ms Kelly said she wanted to stay in the education job
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Education Secretary Ruth Kelly has hinted at a compromise with Labour MPs over school plans for England.
She told the Evening Standard she would "explore" concerns, "especially" on admissions and local authorities' role.
About 90 Labour MPs want safeguards to ensure new independent "trust" schools do not re-introduce academic selection.
Meanwhile Ms Kelly has been holding talks with 25 companies and charities, including Microsoft and KPMG, about sponsoring trust schools.
The meetings are the first in a series of planned seminars with private sponsors and head teachers about the controversial plans to allow sponsorship of schools.
'Loud and emotional'
In the Evening Standard Ms Kelly wrote that "some of the voices against our proposals are loud and emotional".
"But most of my colleagues have more measured and specific concerns about the detail, especially on admissions and the role of local authorities, and I will continue to explore these areas with them," she said.
A Downing Street spokesman said: "We are in a process where people are contributing to the debate."
He added that Education Bill, due to be published in February, would "reflect" this.
The Education White Paper, published last year and seen as central to Tony Blair's third term in office, proposes setting up independent "trust" schools, with more say over admissions.
More than 90 Labour backbenchers, fearful that this could lead to academic selection "by the back door", have signed up to an alternative version.
MPs' reports
It calls for the existing national schools admissions code to be incorporated into law, which the government says is unworkable because of the detail involved.
Meanwhile, a Commons education select committee report is calling for a "new vigorous role" for local authorities in monitoring admissions and "benchmarks" for numbers of children schools take from poor backgrounds.
Tony Blair's spokesman has welcomed this as a "serious piece of work" that ministers might "refine".
However, Tory members of the select committee have published a "minority report", urging the government not to water down plans.
Conservative leader David Cameron has promised to support trust schools.
But Mr Blair wants the plans to get through Parliament without having to rely on opposition backing.
On Sunday, former education and home secretary David Blunkett said the controversy had become "a seminal moment in politics".
Former health secretary Alan Milburn said there was a "huge amount of common ground" between ministers and the backbench opponents and he was "pretty convinced" a good compromise could be found.
To shelve the plans completely would be to inflict a "huge wound" on Labour, he added.