A bid by West Germany's huge Thyssen industry group to take over the Michigan-based Budd Co. may be the largest single deal thus far in the booming investment by West Germans in American companies, according to both German and U.S. officials.

The board of the Budd Co. - makers of railroad cars and truck trailers - approved the merger in principle yesterday. If Budd shareholders add their approval, it will mean $290 million acquisition for the German firm, a Thyssenspokesman said today.

Although other West German industrial giants have, over the years, made cumulative investments in U.S. firms greater than that figure, the proposed new deal is said to be either the largest, or among the largest, one-shot investments.

The proposal comes some three months after the $215 million bid by Germany's chemical giant, Bayer AG, to take over Miles Laboratories, which makes Alka-Seltzer, and at a time when the continuing weakness of the dollar on foreign exchange markets makes investment in the United States a bargain.

Thyssen officials, however, insist that the bargain-priced dollar these days is not the key in mind that if you make money in the United States with dollar investments, the return is also in cheap dollars rather than deutschemarks," the strong German currency.

The chief reason for the offer for Budd, they say, is to move the huge conglomerate - which last year had sales as a group of almost nine billion - away from its heavy and traditional dependence on steel production, which last year accounted for about 35 per cent of sales.

Thyssen, like the rest of Europe's steel industry, is faced with steadily dropping sales, production and sizeable layoffs.

In 1976, the firm dropped from sixth to ninth place among the world's largest steel companies. Despite this, the spokesman claimed that Thyssen "would definitely not try and force a merged Budd Co. to use Thyssen steel in its products.

Thyssen's explanations aside, however, it seems clear that the 20 per cent decline in the value of the dollar against the deutschemark over the past two years has had a major effect in a surge of German investments in the United States.

In sharp contrast to earlier times, West German investment in the U.S. for the past three years has surpassed U.S. investment here and is now believed to be running at about an $800 million a year clip. Those are official estimates.

The real figures are probably a great deal higher when countless, small real estate investments are included and when anonymous funds handled through Swiss banks or Liechtenstein holding companies are added.

For the big West German firms, expanding investment in U.S. companies is a natural way to stay in what is the world's largest consumer market, especially at a time when German labor costs are higher than American costs and when German goods are being squeezed by their high price in the U.S.

Indeed, the dozens of American state and local authorities represented here are scrambling to sign up as many German firms as they can find to help pump up the local economy and employment situation back home.

But there is also a thin line that worries both U.S. and German officials if it is crossed. That involves potential union reaction in the U.S. especially if it is prerceved that German firms are tending to avoid union shops, or possible uncertainty over the long run within the U.S. as to the effects of foreign ownership or management on U.S. companies or employees.

West Germany is generally ranked third or fourth now in terms of annual investment in the U.S., behind Japan and Canada in terms of value and behind Britain as well in terms of frequency of major investments. Iran also is catching up.

Large numbers of small investors here also are being attracted by advertisements by agents for U.S. real estate, in German newspapers and are calling up U.S. consulates in record numbers to get advice.

Many cite political reasons, a fear of creeping socialismm or of a Germany surrounded by Communist governments to the East and West. But veteran U.S. officials here beliieve that at the bottom of that remains economic reasons.

"We are getting a heavy number of calls from people who simply want to buy anything in the U.S. because it's a bargain," one says.