The American Stock Exchange, concerned about increasing competition in the international securities business, yesterday sought to make it easier for foreign companies to qualify for Amex membership.

The board of governors proposed a far-reaching modification of Amex rules that would permit foreign companies to be traded on the exchange without meeting current listing standards. In place of these rules, the Amex would be allowed to consider overseas business customs and practices when deciding on a foreign company's application. The rules changes bring a new principle of flexibility to the listing decisions.

The Amex proposals come at a time when some stock exchange rules have come into conflict with changing corporate practices and desires. The New York Stock Exchange currently is considering a change that would permit companies to have two classes of common stock with unequal voting rights, instead of the single class now required.

The Amex modifications would take place in three main areas: shareholder voting rights and the election of independent directors; quorum requirements, and quarterly reporting. Many foreign companies file only semiannual and annual reports and thus dislike the Amex requirement for quarterly filings.

The Amex plan would require foreign companies to report to American shareholders twice a year and to provide English translations of their financial statements. The Amex also would take a flexible approach to the other fairly rigid requirements that apply to American corporations.

When it comes to quorums and shareholder voting rights, an Amex spokesman said, many foreign companies operate in a totally different way and could not meet current requirements in these areas.

The proposed Amex rule changes are subject to approval by the Securities and Exchange Commission; the SEC also would approve the registration of any foreign stocks being listed by the exchange.

The Amex currently lists 51 foreign companies, of which 33 are Canadian, out of a total of 800 firms.

The proposals, the spokesman said, grew out of a recognition by Amex that the securities business was becoming increasingly international in flavor. "We see no reason," he said, "to deny companies worldwide the opportunity to trade" on the Amex. Although the exchange has been battling with the NYSE and the over-the-counter market for listings, the new proposal was "part of the competitive picture worldwide," the spokesman said.

There continues to be discussion, he said, of the possibility of 24-hour trading.