Chairman Richard G. Lugar (R-Ind.) of the Senate housing subcommittee is proposing a $5 billion program to help reduce mortgage interest payments of home buyers over the next five years in an effort to revive the devastated housing industry and reduce unemployment.

Lugar is scheduled to describe his proposal in a speech in Indianapolis today.

The beleaguered housing industry has been pressing for special federal help all year. The Reagan administration so far has rejected such subsidy plans, but a spokesman for Lugar, the key Republican in Congress on housing issues, said he believes the White House will not oppose this plan.

The nation's homebuilders called for a mortgage rate subsidy at their national convention in January, and said yesterday that they will enthusiastically support the Lugar bill.

While Housing and Urban Development Secretary Samuel R. Pierce Jr. said at the January convention that such a costly program would not be acceptable to the administration, housing industry officials said they have seen signs that the administration may be changing its mind.

The White House had no immediate comment on the Lugar proposal. Pierce was said by an industry official to be inclined more toward other kinds of aid, but willing to forward a mortgage subsidy plan for discussion within the administration.

Under the proposal up to 450,000 low- and moderate-income families would get aid. On newly built homes only, the government would pay part of their interest for five years; the government payments would be up to four percentage points. The buyer eventually would have to repay the government the full amount of the subsidy when the home was refinanced or sold.

The funds would be targeted to areas in economic distress with high unemployment, such as areas of the Midwest reeling from the crisis in the auto industry. Families with incomes of up to $30,000 a year would be eligible to receive the aid.

With a current FHA rate of 15 1/2 percent, a government buydown to 11 1/2 percent would reduce monthly payments from $848 to $644 on a $65,000 mortgage, Lugar said.

When the home was sold or refinanced the family would owe the government $12,754 on this loan. With the rate reduction, 7.8 million more families would be able to afford a home than now can, he estimated.

The Lugar spokesman, Mark Helmke, said the idea has been discussed with a Cabinet-level task force appointed by President Reagan last month to come up with help for housing by the end of March, within the framework of the president's economic recovery plan.

"No one can question Lugar's support from the economic recovery program," he said. "I don't think the president will oppose it Lugar's bill ."

One factor in its favor is the eventual recapture of the $5 billion in aid. At the same time, it would add $1 billion in spending to the fiscal 1983 budget.

Lugar argued that the program would stimulate more than 300,000 new construction jobs and 400,000 jobs in related industries. Tax revenues generated by the new jobs and economic activity would offset about $2.5 billion of the cost, he said.

Unemployment in the construction industry is about 18.7 percent, more than double the overall jobless rate.

"This is a temporary, emergency action to create jobs now," Lugar said in a statement. "Housing has always led us out of a recession before, and it will do so again with this program."