Chrysler Corp.'s cash reserves have been seriously eroded by the continuing depression in auto sales, heightening concerns about the company's survival as Chrysler officials intensify appeals to the Reagan administration for relief from high interest rates.

Chrysler Chairman Lee A. Iacocca met privately Friday with Treasury Secretary Donald T. Regan, chairman of the government board that has approved $1.2 billion in federally guaranteed loans to the company. Iacocca warned the administration that Chrysler and thousands of other dealers, suppliers and producers in the industry are in a day-to-day battle to stay alive, sources said.

Auto sales for the first 10 days of October were at the lowest rate in 23 years, as the introduction of the 1982 models had almost no impact on the car market. To revive sales, auto companies and dealers have had to lower new car prices and financing costs another big notch, cutting harder into future profits.

The impact of the deep sales slump since last spring will show soon when Detroit's Big Three announce third quarter financial results. "You're going to see some lousy third and fourth quarter reports for the whole industry," said Chrysler Vice President Wendell Larsen. At the beginning of the year, Chrysler had forecast a $38 million loss for the third quarter. Instead, the deficit is expected to soar over $100 million.

"There is no question cash is tight," said Larsen, responding to questions about Iacocca's meeting with Regan.

A spokesman for Regan said the administration is not considering any special help for the auto industry.

Chrysler's operating plan for 1981, approved at the beginning of the year by the government's Chrysler loan board, assumed that Chrysler would end the year with a $350 million cash cushion, on top of the $100 million-$150 million in working cash that the company needs to pay suppliers and run its business day to day.

Unless auto sales improve dramatically that cushion will be gone by year's end, forcing the company to live hand to mouth on its operating cash with no reserves in the event of new setbacks, according to well-placed sources.

"I'm not saying they can't pay their bills, but they're really going to have to sweat," said one source familiar with Chrysler's position who asked not to be identified.

Larsen said Chrysler's condition isn't critical, but the need to keep cash flowing into the company far outweighs any other consideration. "Nobody is going for profits now. Everybody is going for cash," he added. Chrysler, along with its U.S. competitors, has been forced into another round of costly rebates and interest rate concessions to keep the cash coming in.

Iacocca told reporters last month that Chrysler's strategy now is almost a "profits be damned" approach as it struggles to stay solvent. It has frozen prices on its most popular 1982 models at 1981 levels and is limiting overall new car price increases to 3.7 percent, or $306 per car, less than half of its original goal.

Larsen said Chrysler isn't asking for additional loan guarantees, or any other form of assistance requiring congressional approval, such as a deferral of more than $400 million in government-mandated payments to its pension plan, due next year. Chrysler's shrinking cash reserves forced it to delay a $260 million pension fund payment scheduled for last month until 1982.

"They aren't talking about additional relief for themselves," agreed Rep. James J. Blanchard (D-Mich.). At the least, Chrysler and the industry must have the kind of credit infusion that Congress and the administration provided to the savings industry, Blanchard said.

"If the current market continues, you're talking about a lot of suppliers going bankrupt, and dealers too, healthy ones, not just the marginal ones. And you're certainly seeing Chrysler and Ford in trouble," said Blanchard.

The potential casualties include International Harvester, the truck and farm implement manufacturer, which lost $397 million in its 1980 fiscal year and may have lost another $225 million in the past 12 months, according to industry analysts.

Three months ago, the auto industry broke out the champagne as Chrysler and Ford joined General Motors in reporting profits for the second quarter--Chrysler officials handed out souvenir bottles of black ink to commemorate the achievement. That euphoria is gone now, washed away by persistent high interest rates and empty showrooms.

If the sales slump continues well into 1982, it would pressure General Motors to cut back further on its ambitious product plans for the 1980s and do the same to Ford's, undercutting its hopes of remaining a full-fledged competitor with GM in the U.S. market.

Chrysler would simply run out of money sometime next year if sales remain flat, some analysts say.

When the government loan board raised Chrysler's guaranteed loan fund to $1.2 billion in the beginning of the year, it had to determine that Chrysler could continue as a going concern, without further federal help, after December, 1983. That goal appeared within reach, assuming Chrysler got a 10 percent share of the U.S. auto market this year--including imports--and total U.S. market sales hit 10 million.

Instead, auto sales will be around 9 million, and even though Chrysler has achieved a 10 percent share, the volume is far below the 1981 operating plan.

"Of course we're below the operating plan," Larsen said. The Treasury's scenario for 1981 assumed that the prime interest rate would drop to 13.5 percent. Instead, it has hovered near 20 percent most of the year, leaving auto financing charges at more than 15 percent.