It could be another of those corporate donnybrooks as one company stages an all-out fight for control of another. Or we could be watching a skilled, sly corporate raider at his foxiest: forcing a threatened management to either buy out his sizable stock position in its company at a fat profit or to seek a friendly takeover by a white knight (at a hefty price above market value).

The prey: Armstrong Rubber Co. of New Haven, Conn., the nation's sixth largest tire manufacturer (1979 sales: $394 million).

The pursuer: corporate raider Carl Icahn, 44, the aggressive head of the New York brokerage firm of Icahn & Co.

Icahn & Co. quietly has acquired roughly 80,000 Armstrong shares; that's equivalent to just under 5 percent of the 68-year-old tire company's approximately 1.7 million shares. I'm also told that Icahn seriously considered making a tender offer for about half of Armstrong's shares, but backed off, perhaps only temporarily, when the stock recently jumped in price.

Last Thursday, for example, when the Dow Jones Industrials were battered for a loss of more than 18 points, Armstrong's shares jumped 2 to 21 1/4 in brisk trading. The reason: a leak about Icahn's purchases coupled with speculation that it would make a run on the company. At press time, Armstrong's shares were trading at around 21 1/2.

The wily Carl Icahn refuses to talk about Armstrong -- even to acknowledge that his company owns any shares. But some sources close to Icahn (who also hold Armstrong's shares) insist he isn't about to sit still . . . which would be totally out of character for him. They believe he wants the company -- and badly. But I'm told that another possibility is that Icahn -- should he not seek a takeover of Armstrong -- could sell his stock to another would-be wooer of the tire company.

At first glance, Armstrong hardly seems an attractive takeover candidate. Granted, its shares are selling at about a paltry five times earnings -- but the tire industry has more than its share of problems. There's a lot of excess capacity in the industry, leading to plant closings and layoffs. People are driving less because of higher gas prices, and this is bound to hurt demand for replacement tires, Armstrong's chief business. Profit margins are under pressure from escalating raw material costs. And a slowing 1980 economy could produce flat earnings this year. (The company earned $4.39 a share last year).

Still another force to be reckoned with is Sears, Roebuck, which owns just under 10 percent of Armstrong's stock. More important, Sears accounts for about 45 percent of Armstrong's annual volume.

Another fair-sized chunk of Armstrong stock (5.6 percent) is held for investment by the Chase family of Hartford.

Considering all the potential negatives, why is Armstrong attractive to Icahn?

For one thing, its stock is selling way below the company's book value of close to $70 a share. Further, the replacement costs of its fixed assets run twice that figure. And some sources suggest that the company's 50 percent interest in Copolymer Rubber & Chemical is in itself worth considerably more than the current market value of Armstrong's shares.

"It's a beautiful situation . . . an asset play that's way undervalued; so why shouldn't Icahn make a run for it?" asks one source.

Icahn himself is unpredictable in his stock-acquisition activities, so there's no guarantee as to what he will do. Last year, for example, he took a stock position in Baird & Warner (now Bayswater Realty & Investment Trust) and later staged a winning fight for control of the company. At last count, his firm held nearly 50 percent of the shares.

In his next two efforts, he didn't get either company. But there's no need, thank goodness to feel sorry for the man; he walked away with an aggregate profit of roughly $5 million.

What does Armstrong (which has never been contacted by Icahn) think about all of this?

The word from Lewis Jolly, financial vice president, was direct and to the point.

"If someone's after us, we don't know about it; in any event, we don't want to be acquired . . ."