Kirk Kerkorian, the high-rolling investor businessman who owns just under half of Metro-Goldwyn-Mayer Inc., announced yesterday he plans to make a cash tender offer of $24 a share for approximately 20 percent of Columbia Pictures Industries Inc.

Kerkorian already has accumulated approximately 490,000 or 5.5 percent of Columbia's outstanding stock, so a successful tender offer would make him by far the largest single shareholder of Columbia, with control of one-quarter of the company's stock.

However, Kerkorian said in a statement that he has "absolutely no plans to seek working control of the corporation," and expressed "confidence in the present Columbia management."

A filing with the Securities and Exchange Commission made jointly by him and his wholly owned Tracinda Investment Corp., which will make the offer, also said Kerkorian has "no plans or proposals," to make "any change in the present board of directors or management," of Columbia.

Wall Street observers noted that Kerkorian always has gone for control of every company he has invested in, and always could change his mind in the future.

But Columbia President Francis Vincent Jr. and Matthew Rosenhaus met with Kerkorian yesterday morning at the Company's Fifth Avenue headquarters and elicited similar assurances.

Afterwards, they indicated they would not oppose his offer but said this would have to be decided by the full board following a detailed study of the proposal.

Allen, president of Allen & Co., the investment banking firm that holds about 7 percent of Columbia's shares, said he was told by Kerkorian that he is "categorically not going for control," and that former Columbia President Alan Hirschfield, who was dumped by the board in July, "has no part in this."

Allen said current insiders, who together control about 30 pencent of Columbia shares, will not tender to Kerkorian. And he said Kerkorian had agreed that, if he ever sells his 25 percent stake, he will give Allen and the other insiders who now run the company the right of first refusal.

"I think from our point of view we are gratified and pleased by his expression of confidence in the company and its management," said Vincent. "We think it is a positive reflection on the company and us."

Kerkorian might have more trouble with the Justice Department in Washington because, if he succeeds, he would become the controlling shareholder in two of Hollywood's six major studios which together account for 80 percent of the motion pictures that are released.

MGM, however, has gone out of the distribution business entirely and has subordinated its movie production activities in recent years to such ventares as the Grand Hotel in Las Vegas. Lawyers for Kerkorian said they believed filings with the Justice Department and Federal Trade Commission would satisfy antitrust objections.

"We've studied the situation and feel very comfortable that this does not violate the antitrust guidelines," said Stephen Silbert, an attorney with the Los Angeles firm of Wyman, Bautzer, Rothman & Kuchel.

Columbia is just emerging from a year that included both record profit and disclosures that the former head of its studio, David Begelman, embezzled more than $60,000 from the company. The Columbia board fired company president Hirshfield in the aftermath of the Begelman affair.

Hirshfield had wanted to dump Begelman, but reconsidered after key board members such as Allen and Rosenhause opposed him. Begelman eventually quit after publicity about his forged checks ignited a widespread debate about Hollywood business ethics and practices. And the split between Hirschfield and the board never healed.

Reports continue of morale problems in the operating divisions of Columbia, which besides the movie and television operations, include Arista Records and D. Gottlieb & Co., a pinball manufacturer.

Columbia shares yesterday gained 2 7/8 to 20 7/8 on the New York Stock Exchange, where the stock was on the most active list.

If the tender offer proceeds, it would not take place until January, Kerkorian indicated.

According to the SEC filing, Kerkorian owns 48 percent of MGM's stock - 42 percent through Tracinda and the other 6 percent in his own name. It said he used "his own general funds" to buy his initial 5.5 percent Columbia stake, but did not indicate how he will finance the $24-a-share tender offer.