The Trilateral Commission - the David Rockefeller-founded group many of whose members moved into influential positions in the Carter administration - is considering a merger with another heavyweight, private organization of prominent international movers and shakers.

The commission's prospective merger partner is the Paris-based Atlantic Institute, an organization that isn't exactly a household name in the circles where most people move.

But, in that special arena where global thinkers, multinational business executives and politicians rub against each other in an effort to influence world events, the move has potentially large significance. Its impact is roughly comparable to the effect in business circles of, say, General Motors joining forces with Volkswagen.

If the merger goes through, it's likely to trigger some new versions of the conspiracy theories heard a year ago when so many Trilateral Commission members turned up in key jobs within the Carter administration. That caused both left-wingers and right-wingers to speculate about the commission being a mechanism for infiltrating the government.

President Carter was a member. So, too, was Vice President Mondale; and Carter's national security adviser, Zbigniew Brzezinski, had been a director of the commission.

Other Trilateralists in the administration include Secretary of State Cyrus R. Vance, Treasury Secretary W. Michael Blumenthal, Defense Secretary Harold Brown. U.N. Ambassador Andrew Young, Deputy Secretary of State Warren Christopher and Under Secretary of State Richard N. Cooper.

With these men standing astride the main channels of foreign policy, and with other Trilateralists only a notch or two below them in the administration, those who like conspiracies seem certain to read some sinister new meaning into the commission's move toward merger with the Atlantic Institute.

Not so, says George Franklin, the Trilateral Commission's coordinator. The merger talk, he explained yesterday, is prompted by the fact that the two organizations overlap in many areas of interest, activity and membership. By getting together, he added, they might be better able to avoid wasteful duplications of effort and - by no means an incidental consideration - competition in raising funds.

What's more, Franklin stressed, a merger is by no means certain. The two organizations, he said, are only just beginning to explore the idea and, even if they come to an agreement approved by both their memberships, nothing is expected to happen for several months.

As he points out, both organizations are remarkably alike in many important respects. The Trilateral Commission, which was founded by David Rockefeller in 1973, has been described as a "sophisticated establishment Rotary Club" and a "floating seminar for business and academic and political leaders."

Its members are mainly establishment figures recruited from North America, Western Europe and Japan. Every nine months or so, they get together on one continent or another to tilt verbally at world problems: and the commission hires academic experts to turn out weighty studies on the subjects that interest the members.

The Atlantic Institute is, in many key aspects, an almost interchangeable organization. It is directed by Martin Hillenbrandt, former U.S. ambassador to West Germany, and, as one Trilateral staffer notes, "At any given time, there's probably an overlapping group of 10 to 20 individuals who hold membership in both."

However, the two groups are not identical. The Trilateral Commission tries to suggest policy options on a variety of topics, while the Atlantic Institute is geared more toward instituting and subsidizing research on economics problems.

Despite a common supposition that the commission is subsidized by the Rockefeller family, both organizations actually obtain the bulk of their operating funds from tax-exempt foundations and corporate gifts. Inevitably, that means competition for the available money; and, as Franklin noted, that, in turn, is a spur to merger.