The Dodge Omni and the Plymouth Horizon may have serious stability and handling problems, according to a report in an upcoming issue of Consumer Reports.

Informed sources say the magazine will rate the two subcompact automobiles "not acceptable," a rating that has not been given to an American-made car in "at least a decade," according to a spokesman for Consumers Union, publisher of Consumer Reports.

Late yesterday a Chrysler spokesman released the following statement in response to questions about the CU findings:

"There is no handling problem with our new Omni and Horizon cars. As a matter of fact, the cars' steering and handling has received enthusiastic praise from professionals and consumers alike. Chrysler has built millions of front-wheel-drive cars in Europe [Simcas] and has received awards both here and abroad for these vehicles."

When the two front-wheel-drive models were introduced late last year, Chrysler officials said they hoped the cars would help to stop the slide in the financially troubled manufacturer's share of the market.

Consumers Union has scheduled a press conference at 2 p.m. today to announce its findings and show a brief film of the test used to determine that the cars had handling problems.

The organization is the largest and second-oldest independent product-testing institution in the country. It publishes a consumer buying guide in addition to its monthly magazine.

Motor Trend Magazine recently named the two cars, which are virtually the same in design, "Car of the Year."

The two cars, the first American-made subcompacts with front-wheel-drive, have been selling exceptionally well, with more than 110,000 Horizons and 55,000 Omnis purchased since they were put on the market in January. Those sales have given Chrysler 21 percent of the domestic subcompact market, up from zero only six months ago.

An the Chrysler officials say they are turning out 1,120 of the vehicles a day at their Belvidere, III., assembly plant, almost 200 a day more than usual top-speed production.

The sales success of the Omni and Horizon has come at the expense, to a great extent, of the Ford Motor Co. Problems with recalls and consumer complaints have caused Ford's share of the subcompact market to drop from 53 percent in April 1977 to 33 percent last April.

Another extremely important benefit of the Omni and Horizon is their gas mileage figures. With a manual transmission, the cars, which use Volkswagen engine, tested at 25 miles per gallon for city driving, 39 mpg highway and 30 mpg composite, according to the Environmental Protection Agency.

Without those figures, Chrylser's corporate fuel economy average for 1978 cars would be 17.8 mpg, short of the 18-mpg average required by law - a situation that would make the company liable to millions of dollars in fines. With the two cars, Chrysler averages 18.6 mgp.

Chrysler has already had safety problems with its Dodge Aspen and Plymouth Valare models. Introduced two years ago, they were recently recalled for the fourth time.

Consumers Union said it purchased and tested three different models of the cars in question, each with different extras, and borrowed a fourth with a special heavy-suspension option. Although the consumer group would not officially confirm last night that the Omni and the Horizon were the cars tested, CU spokesman Ira Furman did say the motor company involved had participated in some of the testing.

A spokesman for the National Highway Traffic Safety Administration said the federal government was not presently investigating the Omni and the Horizon for any safety defects.