The Reagan administration will propose next week revamping the nation's largest federal education program to allow poor parents to use federal money to send their children to private schools.

Under the proposal, called The Equity and Choice Act or TEACH, the parents of the 5 million American children now eligible for remedial help under the $3.2 billion "Chapter I" program would be able to receive federal money in vouchers, averaging about $600 each. The money could then be used to pay the tuition at a private school, or to pay for remedial services offered at a public school.

Local school districts would continue to receive Chapter I money under the proposal, but parents would be able to take some of it away from them by requesting a voucher instead of using the standard program provided by the local schools.

Education Secretary William J. Bennett is scheduled to unveil the plan at a news conference next week. A copy of the proposal was obtained yesterday by The Washington Post.

A department spokesman said yesterday there will be no comment until the plan is formally released.

This will mark the administration's second major push for a voucher plan, a favorite proposal of President Reagan, Bennett and conservative education groups. But voucher plans have always run into strong opposition from the professional education lobby, from teachers and on Capitol Hill, where opponents fear such a proposal would hurt the public school system while forging a new financial link between government and private schools.

By proposing a voucher plan specifically for the Chapter I program, which gives money to school districts to aid educationally deprived children, Bennett is trying to portray his proposal as aimed at the poor, minorities and disadvantaged.

In a draft copy of a letter to House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), Bennett said this latest voucher proposal would improve educational quality and "serve the cause of social justice by providing disadvantaged families some of the educational choices already available to more affluent families."

"It would improve the quality of Chapter I services," he said, "by increasing parental involvement in the program and by promoting healthy rivalry among schools to meet the needs of disadvantaged children."

Signed 20 years ago by President Lyndon B. Johnson, Chapter I of the Elementary and Secondary Education Act now represents almost a quarter of the Education Department budget, and has become the primary symbol of the national commitment to educate the poor.

Much of the program -- formerly known as Title I -- was thrown into chaos last July, when the Supreme Court ruled that money for it could no longer be used to pay public schoolteachers who went into religious schools after hours to give remedial classes to the poor. At that time, Bennett blasted the court and vowed to introduce a voucher plan for Chapter I that could "pass constitutional muster."

Reaction to Bennett's plan was expectedly harsh yesterday, as copies of the unreleased report began circulating in Washington.

"It's a ridiculous proposal," said Michael Casserly, legislative director for the Council of Great City Schools, whose members receive a large share of Chapter I money. "This would hurt the public schools and it would be an utter disaster for the Chapter I program."

"The bill's a Trojan horse," said Michael Resnik, associate executive director of the National School Boards Association. "It carries the great appeal of parental choice, but if it's enacted -- which I doubt it will be -- it would diffuse services for kids."

"To say it's going to be used to help the disadvantaged and the poor is an insult," said Millie Waterman of the National Parent-Teacher Association. "It's offensive to us and we will oppose it."

The National Education Association and American Federation of Teachers repeated their positions that a voucher plan would undermine support for public education.