Warner Communications Inc., concerned about the labor situation at the ailing New York Daily News, has abandoned its interest in acquiring the newspaper, a top Warner executive said today. Warner's decision reportedly leaves former Washington Star owner Joe L. Allbritton as the leading candidate to buy the newspaper.

Several sources say that Allbritton is negotiating the acquisition with the Tribune Co. of Chicago, which owns the News. The Tribune Co., a communications and entertainment conglomerate, announced Dec. 18 that the New York tabloid was for sale.

Warner, a New York-based conglomerate, began investigating the possible acquisition of the News almost immediately after it was put up for sale.

Martin Payson, general counsel of Warner, said today that his company backed off because of potential labor problems. "We don't see how any potential buyer can deal with the unions when they're not the buyer of last resort," Payson said.

Warner reportedly reached this conclusion on the advice of two outside consultants hired to look into the acquisition of the News.

A spokesman for Allbritton Communications Co. in Washington would neither confirm nor deny the reports that Allbritton was negotiating to acquire the News. But one source familiar with Allbritton's efforts say that he is acting as if he is determined to acquire the News. Payson would not comment on the Allbritton reports.

Late last year, Albritton acquired the Trenton Times from The Washington Post Co. He owns two other New Jersey newspapers, the Hudson Dispatch in Union City and the Patterson News in Patterson.

Earlier last year, Allbritton acquired control of Riggs National Bank and assumed the chairmanship of the bank holding company.

The Tribune Co. announced it would sell the News, the nation's biggest circulation general interest paper, after it lost $12 million in 1981. High labor costs have been among the reasons cited for the News' recent poor performance.

Monday night, three of the News' 11 unions voted to put a March 31 10 percent wage increase into escrow and to make the funds available to help save the newspaper from going out of business.

George F. McDonald, president of Allied Printing Trades Council, which includes the 11 unions represent some 3,800 News employes, said he expects some of the other unions to vote soon on the escrow plan.

McDonald estimated that the escrow fund could generate about $10 million for use in helping the News.

So far, no potential buyer has approached the unions for concessions that everybody agrees must be part of a sales package, according to an attorney for the unions.

Les Bridges, a News vice president, said it was still too early in negotiations for such talks to take place. "Things have to firm up before a dialogue starts with the unions," Bridges said.

In addition to Allbritton, American Stock Exchange Chairman Arthur Levitt Jr. has been negotiating with the Tribune Co. Sources familiar with those negotiations say that one of the sticking points is the Daily News building. Levitt wants not only the newspaper but the building itself.