Henry Fairlie, a British journalist who has built his reputation in the United States writing about the American scene in such publications as The Washington Post and The New Republic Magazine, has lived in this country for more than 10 years as an illegal alien, according to immigration officials.

Fairlie, who told a U.S. Immigration and Naturalization Service investigator that he misplaced his British passport several years ago, technically has been given until March 9 to leave the United States voluntarily. But, INS officials said, he has several options available to him and may receive extensions of his departure date until he can successfully legalize his immigration status.

Fairlie told the immigration service that in 1975 he walked into the Denver district office of the INS to try to straighten out his status. He said that he filed the proper forms at the time, but an INS spokesman said yesterday that ther was "no record" of such an application. It is not clear whether the forms were lost, thongh many are each year, according to INS officials.

His case was brought to the attention of the Washington INS office earlier this year when staffers in Denver noticed his whereabouts and, on examining his file, discovered that he had been ordered to leave the country in 1976.

Fairlie was admitted to the United States in 1966 on a journalist's visa that, according to a spokesman for the INS, normally would expire after one year. In Fairlie's case, the spokesman said, it apparently was never renewed. Since its expiration he has been, in immigration jargon, "out of status" -- that is, an illegal alien.

Fairlie eventually could be deported, but INS officials said yesterday that the chances of that happening now are relatively slim.

The officials pointed to several aspects of Fairlie's case that may work in his favor: he has lived in the United States for more than seven years, he has told the INS he has a daughter living here who is a legal permanent resident and he may be able to demonstrate that he has unusual skills not readily found in the American work force. Under current laws any one of these factors could enable him to legalize his status.

Fairlie has cooperated fully with the INS since he was ordered to appear for an interview on Feb. 9, officials said.

Though reluctant to talk about his situation yesterday, Fairlie said, "I reject the idea of a problem [with immigration]."

He said he told a few close friends that he was having some difficulties and, "As everyone points out," he said, "I've hardly been hiding myself."

Since he came to America, the 55-year-old Fairlie has published several books, including "The Kennedy Promise," "The Spoiled Child of the Western World," and most recently "The Seven Deadly Sins." He has regularly published articles in numerous magazines, written a semimonthly column for The Post's Outlook section and is a contributing editor for the new Republic.

Fairlie said that while he was living "overground-underground" he never acquired a social security number, never even opened a checking account because of all the questions asked on the application forms.

"It's very difficult to live out of status," Fairlie said."I used to look at those figures [estimates of the number of illegal aliens in the United States] -- 12 million, and think, 'Who are the other 11,999,999?'"

Now, he said, he hopes eventually to become an citizen of the United States. "I've written this and it's true," he said, "It's my home."