The Reagan administration's latest economic forecast, to be released next week, sees a virtually stagnant economy for the rest of this year.

Unemployment is expected to rise to 7.7 percent by the fourth quarter from its present 7.3 percent, interest rates should begin to fall and a continued slowdown in inflation is excepted, sources said yesterday.

But the latest numbers showed that the administration is sticking by its original optimistic view of the economy from 1982 on.

Its forecasts of a growing economy coupled with declining inflation have been labeled a rosy scenario by many outside economists. This skepticism has been reflected in the financial markets, where interest rates have remained stubbornly high.

By next year, the Reagan forecast predicts that the economy will pick up speed, while inflation and interest rates will remain on a downward path. And by 1984 inflation is predicted to be running at only 5.2 percent, while economy grows at 4.5 percent in real terms, and unemployment averages 6.2 percent of the labor force.

The latest figures take into account the much higher than predicted interest rates, faster growth and lower inflation that have occurred in the first six months of this year.

The economy is now expected to grow by 2.6 percent during 1981, compared with an original forecast of 1.1 percent for the year as a whole rather than 11.1 percent. However, all the growth in the economy came in the first quarter of this year, and the administration now expects little change in real output between now and year's end.

Contrary to the predictions of some private economists, the administration does not expect any negative quarters (an actual decline in output) the rest of this year, the sources said.

Starting in 1982 unemployment, according to the Reagan numbers, will decline steadily from 7.6 percent of the work force in the first three months of the year to 7.0 percent by year's end, sources said.

Many private economists are less optimistic, believing that the Federal Reserve Board's tight money policies will keep the economy from growing very rapidly and unemployment from coming down. Real growth will average 3.4 percent next year, down slightly from the original 4.2 percent estimate.

Administration officials say that Reagan's tax and spending cuts together will bring down interest rates and inflation while leaving room for economic growth.

Interest rates have remained high so far this year and the new forecast reflects this. Three-month Treasury bill rates are expected to average just over 13.5 percent for 1981, rather than the 11.1 percent rate predicted in February.

However, officials believe tht rates will begin to fall very soon from their present level of almost 15 percent and will slide quarter by quarter during 1982, dropping to 9 percent by the end of the year.

This still leaves a 10.5 percent average Treasury bill rate during the year, up from an original projection of less than 9 percent.

The higher than expected interest rates will push up federal spending this year and next, but because of a delayed tax bill the budget deficit numbers for 1981 and 1982 are not expected to be changed very much, sources said. This year's budget gap is expected to be higher than the $51 billion to $52 billion predicted recently by Treasury Secretary Donald T. Regan.

Another factor putting pressure on the deficit is that tax revenues have been less than expected so far this year. The drop in inflation since January, and particularly lower oil prices, have cut tax receipts, sources said. However, reduced spending on such indexed programs as Social Security will partly offset these pressures.

On of the parts of the forecast that is most likely to be challenged by outside economists shows interest rates falling steadily throughout next year, and thereafter, to as low as 5 percent in 1987.

By then the annual inflation rate, as measured by the consumer price index, is forecast to be only 3.9 percent, real growth is also expected to be 3.9 percent and unemployment at 5.3 percent of the labor force, sources said.

Such a combination of high growth and slowing price rises during the 1980s would make a balanced budget much easier to achieve. The Congressional Budget Office disagreed with the administration's earlier predictions of a balanced budget by 1984, largely because of very different economic assumptions.

The Reagan scnario shows the economy's growth rate peaking at 5 percent in 1983, and slowing year by year. Year by year inflation goes from 9.9 percent in 1981 to 7 percent in 1982, 5.7 percent in 1983, 5.2 percent in 1984, and then 3.9 percent by 1987.