Australian press baron Rupert Murdoch will not ask the Federal Communications Commission to allow him to keep the Chicago Sun-Times and The New York Post when he acquires Metromedia television stations in those markets, a source close to Murdoch said yesterday.

The source said Murdoch has hesitated to make the announcement because of fears distress sales of the two daily newspapers might ensue.

Meanwhile, Howard J. Rubenstein, a spokesman for Murdoch, yesterday said inquiries about the two papers have already come in. "The phones have been busy," he said. "He is considering the offers." Rubenstein declined to identify which companies were interested in buying the papers.

Metromedia Inc. announced Monday it will sell its chain of major independent television stations, including WTTG-TV 5 (channel 5) in Washington to Murdoch and Denver oilman Marvin Davis for more than $2 billion. The other stations are in New York, Chicago, Boston, Los Angeles, Dallas and Houston.

Murdoch will have to dispose of either newspapers or televisions stations in New York and Chicago to satisfy FCC rules that prohibit any one person or entity from owning newspapers, television or radio stations in the same market.

Yesterday, The Washignton Post reported FCC sources said inquiries had been made on behalf of Murdoch as to whether it might be possible to keep the newspapers.

"They are not going to seek a permanent waiver for The New York Post and the Chicago Sun-Times and are going to comply with the FCC rules," said FCC Commissioner James H. Quello. "The only waiver they will request will be 18 months or two years to dispose of the newspapers in an orderly, non-distress-sale way." Quello, who in the past has stressed FCC rules should be taken seriously, said, "I wouldn't advise them to ask for a waiver , you wouldn't want anything to delay or obstruct the transaction."

The Chicago Sun-Times is well in the black with revenue of about $45 million and profits of about $20 million last year. But The New York Post reportedly has been losing between $15 million and $20 million a year since Murdoch acquired it in 1977.

"Murdoch is deathly afraid of saying he is going to sell those newspapers because he is afraid of creating a distress-sale type of environment," said a source close to Murdoch. "His concern is that he doesn't want to create an environment in which the employes would fear what is going to happen to them." The source added Murdoch did not want to shut the papers down. "He doesn't want to dump them for anything," the source said.

Nevertheless, sources said an announcement is expected today that Murdoch will sell the papers.