With the Transportation Department hoping to announce next week the winner of its Conrail bidding contest, the president of one of Conrail's larger unions said yesterday he favors a management plan to sell the federally owned railroad to the public.

R. I. Kilroy, president of the Brotherhood of Railway and Airline Clerks (BRAC), also rejected the bid of Norfolk Southern Corp., the railroad holding company that is the front-runner for the Transportation Department's endorsement.

Kilroy, however, may not have the allies he needs to impose his views on the rest of Conrail's workers. The presidents of two other major Conrail unions -- O. M. Berge of the Brotherhood of Maintenance of Way Employes and Fred A. Hardin, of the United Transportation Union -- both said late yesterday that the issue of whom labor endorses remains open.

Hardin and Berge together represent a majority of Conrail's 35,000 unionized employes. The railroad has 17 unions.

Further, while the unions have not reached a unified view on whom to support, the Transportation Department received underpinning for its opposition to Conrail management's public sale proposal: Goldman, Sachs & Co., the department's financial adviser for Conrail, has found seven reasons not to like the concept.

"The management proposal is not a firm commitment and there is no assurance that such a transaction can be accomplished," Goldman, Sachs said in a letter to Secretary Elizabeth Hanford Dole.

The letter also said that, to finance its public sale, Conrail would need to borrow $422 million by 1988, a heavy debt burden. "Conrail alone in a public offering scenario is not as strong as Conrail would be combined with another purchaser such as Norfolk Southern," Goldman, Sachs said.

Department officials have made certain that labor representatives have copies of the Goldman, Sachs letter.

A public offering has the virtue, from the point of view of Conrail Chairman L. Stanley Crane, of leaving the Conrail management in absolute control of the railroad, now a moneymaker after consuming $7 billion in tax dollars to get on its feet.

In addition to Norfolk Southern and Conrail management's public offering, there are two other contestants -- the Alleghany Corp., a New York holding company, and an investor group headed by J. W. Marriott Jr., the Washington hotelier.

Kilroy -- whose views on both Norfolk Southern and the public offering have been expressed before in the Pennsylvania press -- held his news conference as negotiations between other union representatives and the Norfolk Southern were continuing.

Kilroy said that "we have been unable to reach with Norfolk Southern an agreement that fairly protects Conrail employes." He stressed that he was speaking for his union, not for the labor task force studying Conrail offers or for the Railway Labor Executives Association, which is to meet Tuesday and decide which, if any, of the offers it endorses. The department is expected to announce its preference later in the week and refer the matter to Congress.

A unanimous labor veto of Norfolk Southern would seriously damage its chances to acquire Conrail, a senior department official conceded yesterday. Norfolk Southern also must resolve a number of competitive questions raised by the Justice Department about an acquisition of Conrail. Neither Norfolk Southern nor department officials believe those questions unanswerable, but Justice has not issued a final report on the antitrust implications of a Norfolk Southern victory. Federal Railroad Administrator John Riley told Congress Thursday that "Justice has taken the position that a sale to Norfolk Southern cannot reduce competition."

Kilroy said he there was nothing "special about the Conrail offer other than that it can deliver restoration" of wage deferrals "quicker than anybody."

Conrail employes are receiving 12 percent less than industry wages. However, all bidders have promised to restore industry wages, retroactive to July 1, 1984, according to informed sources.

Hardin, president of Conrail's biggest union with 12,000 working members, said, "I have not vetoed Crane's plan, but I have little enthusiasm for it." He also said that "Norfolk Southern would bring the greatest financial strength and would insure Conrail forever. There would be some mergers of terminals and a potential loss of some jobs, but Mr. Crane's five-year plan projects a loss of 4,500 jobs, so it all has to be carefully evaluated."