Officials of the Justice Department and the Federal Trade Commission are in the midst of a highly political and potentially bitter battle over which agency will review E.I. du Pont De Nemours & Co.'s proposed $7.3 billion acquistion of Conoco Inc., sources said yesterday.

Citing their expertise in the chemical and petroleum markets, both agencies have proposed reviewing the largest corporate merger in American history during a private meeting yesterday, the sources stated.

Representatives of the Justice Department reportedly told FTC staff members that the case is viewed as a major test of the Reagan administration's willingness to approve merges, particularly among companies in different industries. "This is clearly a big test case for Justice," one source said.

The case is viewed as "symbolic of the administration's efforts to put their imprint on enforcement of the antitrust laws," said one high-level source.

Further, Justice officials told the FTC that because that regulatory agency is operating without a permanent chairman, key staff people might not be with the agency for much longer. James C. Miller III, director of an administration task force on regulation, has been named chairman. If confirmed by the Senate, Miller will replace acting FTC Chairman David Clanton as the agency's top administrator.

In addition, Justice Department officials also pointed out that the FTC, still fresh from successfully fighting off Reagan administration efforts to strip it of all antitrust powers, might be timid in tackling the massive merger while still beset with continuing congressional and administration criticism.

The discussions were characterized as unusual in that Justice Department officials emphasized these political concerns rather than the conventional and historic themes of these talks, such as expertise and staff availability. The assistant attorney general for antitrust, William Baxter, is among several administration officials who have called for elimination of the FTC's antitrust authority.

The matter almost certainly will not be decided at the staff level, so the decision on who will handle the merger will be made by Baxter and Clanton. One expert said decisions on the Justice-FTC review process is rarely made at that level, and another source said these talks had moved to that level only twice in the last five years.

Both Baxter and Clanton are attending an antitrust conference in Colorado and could not be reached for comment.

In a related development, Sen. Howard Metzenbaum (D-Ohio), former head of the antitrust subcommittee, and Sen. Edward Kennedy (D-Mass.), yesterday called on Sen. Strom Thurmond (R-S.C.), chairman of the Judiciary Committee, to hold hearings on the merger.

In addition, the two senators wrote to Attorney General William French Smith and Clanton expressing their concern over the Du Pont-Conoco merger. Metzenbaum and Kennedy told Smith the deal "may raise such a threat to the competitive economy and to the American consumer and small businessperson that this merger should not be approved without the closest scrutiny."

Under established guidelines, officials of the two agencies share responsibility for enforcing antitrust law, and they meet routinely to determine which agency will handle mergers and other related matters.