Several of this city's foremost power players are jockeying for a role in deciding the fate of The New York Daily News, the ailing tabloid that was put up for sale last Friday by its parent, the Tribune Co. of Chicago.

No sooner had the sale been announced than Felix Rohatyn, the investment banker who six years ago spearheaded the effort to save New York City from bankruptcy, was out looking for a buyer. As a partner in the investment house of Lazard Freres & Co., Rohatyn has gained world reknown--and great personal wealth--from putting buyers and sellers together.

Rohatyn, who could not be reached today to explain how he became involved with the News, turned to another influential financial figure, Steven J. Ross, chairman of New York-based Warner Communications Inc.

Warner is a $3 billion entertainment conglomerate that includes interests ranging from Mad magazine and Warner Brothers Pictures to Warner Amex Cable Communications and Atlantic Records. One of Warner's most successful ventures, Atari Inc., manufacturer of video games, is expected alone to earn close to $200 million in 1981.

But disclosure of the Rohatyn-Ross discussion apparently rankled another New York power, Theodore Kheel, the attorney and labor negotiator who for decades has been involved in most of the city's major labor disputes, particularly those involving newspapers.

Kheel is being retained by the Allied Printing Trades Council whose 11 unions represent some 4,000 workers at The Daily News.

Along with Council president George McDonald, Kheel called a press conference today for the apparent purpose of signaling the Tribune Co. and any would-be buyers of the News not to negotiate without consulting the council.

Kheel also disclosed that the council is "investigating the possibility of a purchase by the employes" of the newspaper. He said the council plans to meet Wednesday "to receive expert information on the mechanism of such a purchase."

The announcement of the sale came as a shock to the council, Kheel said, especially since the unions and the News had begun a series of meetings last August to consider the paper's problems.

"At no time did did the News ask the unions for any concessions" before announcing the sale, complained Kheel.

As for the Warner development, Kheel lamented, "We didn't receive a call from Felix Rohatyn . . . even though he knows us very well."

Kheel allowed that he was told by the Tribune Co.'s consultant on the sale, Ira Harris of Salomon Brothers in Chicago, that it will be at least three weeks before the company comes up with a price tag for the News. That led him to conclude, said Kheel, that the premature release of the information was "a public relations ploy."

Warner is just one of several concerns that have expressed some interest in the News, according to a Tribune Co. spokesman.

A Wall Street analyst who follows Warner, David Londoner of Wertheim & Co. Inc., says it is far too early for the company to be considered as even a possible suitor.

"As I understand it, this is in the very preliminary stage," he said, adding, "Warner looks at 15 or 20 deals a month and may do one or two a year."

Kheel noted that in recent months the News, with daily sales of 1.5 million, has enjoyed a surge in circulation and advertising. But it is unclear how much of that is permanent, and how much comes from buyers who want to play the News' high publicized contest called Zingo, which was begun in September for the purpose of adding readership.

Rupert Murdoch's New York Post, the News' arch rival, weighed in with a similar game called Wingo, and it also claims a big jump in readership.

The Tribune Co. reportedly has been losing patience with the News ever since the failure last August of Tonight, the paper's one-year-old, $20 million attempt to challenge Murdoch's exclusive hold on the afternoon market.

The Tribune Co. is privately owned, but it does publish quarterly and annual figures. In 1980, it had profits of $78 million on revenues of $1.2 billion, two-thirds of which came from newspapers.

But the company has failed to keep pace with other big newspaper chains in recent years. The management sought to counter this by introducing tough economic measures to gain better returns from its newspapers, which include publications in the Sun Belt as well as the Chicago Tribune and the News.

In addition to bearing the expense of the News, the company has made $500 million in capital expenditures recently to build a Chicago printing plant, a new plant for its Orlando Sentinel Star and a Canadian newsprint plant. In addition, the company has spent money diversifying. Last summer the company surprised the sports, publishing and financial worlds by acquiring the hapless Chicago Cubs baseball team, a troubled ball club that will be costly to rebuild but that reportedly offers certain tax benefits to the Tribune Co.

It also spent $33 million to buy Douglas Communications Corp., which doubled the size of its cable television operation.