Public grants to private schools in Jersey could be saved if States members vote against the proposals.
Deputy Reed has agreed to allow States members to vote on the proposed cuts to fee-paying schools instead of making the decision himself.
But Deputy Reed said he will not withdraw his plans.
The education minister wants to cut the subsidy paid to fee-paying secondary schools by half as part of wider government savings.
The minister announced he would agree to let politicians vote on the issue, and would spend more time talking to the school governors.
He said he still believed the cuts should be considered.
The minister told the States of Jersey: "I think it is absolutely appropriate that we pursue and continue the dialogue that has only just been started with the schools.
"This will form part of and provide further information to support the development of the green paper I want to bring out in the new year.
"As such I have no intention of withdrawing the current proposal."
But the Deputy told the States assembly that he would be bringing a debate to the House.
He said: "There are no plans to further reduce the grants to fee-paying schools outside of the proposals currently being explored with all fee-paying schools.
"My department is working closely with all schools to achieve a mutually satisfactory agreement.
"Once the discussions are completed I will be bringing a proposition to the States so members will be able to consider this matter with all the information in front of them."