Is the press picking on Boston's Mayor White?

The Eagle Room in Boston City Hall was packed. Kevin H. White, the city's four-term mayor, had scheduled a press conference Jan. 10 to announce a new housing ordinance.

But this time there were no free Danish pastries. This time a burly security guard insisted on seeing press identification. And this time the questions were not about housing, but about the beating the mayor has taken recently in the national press.

''I don't know what warrants that kind of coverage in the Moscow edition of the New York Times,'' he quipped, adding with characteristic wit that ''I'm sure (Soviet leader Yuri) Andropov is now trying to find out who Joie Prevost is.''

The ''coverage'' in question was a front-page piece in the Sunday Times (which circulates internationally and is seen by Kremlin officials) the day before. It reported that two of the mayor's top assistants (Director of Consumer Affairs Joanne Prevost and her husband, chief fund-raiser Theodore Anzalone) were living in a $250,000 house in the city's North End, which Miss Prevost had bought for $1 in 1981. Raising questions about the legality of the transaction, the article reported that the house had been purchased through a ''straw'' owner who was later given the city's permission to develop a nearby waterfront site.

That story is but the latest in a flurry of national attention. City officials note that the Times ran six stories in December (one on the front page) detailing the corruption investigations now plaguing the mayor. Last month ABC did a segment on national television. This month NBC followed suit, and stories appeared in the Washington Post, the Wall Street Journal, Time, and Newsweek.

Why the flap?

The obvious reading is that allegations of corruption in the mayor's administration - where probes are reportedly being undertaken by the FBI, the IRS, the Postal Service, and the US Department of Housing and Urban Development - is a national story. Boston's two decades of resurgence from a dying industrial town to a booming high-technology and professional-services capital is closely tied to the career of its mayor. The national press, watching the one , naturally watches the other. And in Kevin H. White it finds a personality of great interest to readers. The typical portrait is almost a stereotype of a canny Irish charmer - who, beneath the whimsy and moodiness, is a master at political maneuvers.

He is also widely seen as arrogant - and, in the tradition of Massachusetts politicians at least since former Boston Mayor James Michael Curley's day, vengeful. So he has numerous enemies, all of whom would love to topple his empire. One of them is reputed to be US District Attorney William F. Weld, a Republican of Yankee extraction. He has mounted what may be the most serious challenge, in the form of a grand-jury probe into a 1981 birthday party planned by the mayor for his wife, Kathryn. The party, canceled when the state's Ethics Commission showed interest in it, had all the earmarks of an illegal fund-raiser. The commission, which publicly reprimanded the mayor after an investigation, reportedly found evidence of an extensive cash-laundering process - evidence it has turned over to the district attorney.

The mayor accuses Mr. Weld of political motivation. Mayoral aides hint that there could be a direct flow of information from Mr. Weld to Fox Butterfield, the New York Times reporter responsible for many of the recent stories. Such a flow of information, say White aides, would be in violation of law.

But a deeper reading of events leaves observers asking several larger questions:

* Is the Times somehow out to ''get'' Kevin White? The latest story about Joie Prevost, says the mayor, is ''old hash.'' The Boston Phoenix, a weekly, first ran it on Dec. 1, 1981. The city's dailies, the Boston Globe and the Herald American, covered it last March. ''If you people feel that was current,'' the mayor told his press conference, ''then in my opinion the Battle of Bull Run is not over.''

David R. Jones, national news editor for the New York Times, objects, saying that the story contained some new information. Besides, he says, it is ''a story that we think is important, that we haven't developed in the past.'' And many here note that the questions it raises have yet to be satisfactorily answered, even though no charges have ever been brought in the matter.

But Thomas Winship, editor of the Boston Globe, sums up the prevailing view among the local press when he says that ''the New York Times stuff on Kevin White was well done, but did not exactly plow much new ground.''

* Is the Times taking advantage of a vacuum? To many, the Globe (which is Boston's paper of record) appears to be of two minds about its approach to the mayor. At times it has blasted him: An editorial last summer urged the mayor not to run for a fifth term. Since then, however, some longtime readers sense a soft-pedaling of some of the corruption stories.

* Is the Times using such stories to expand its New England circulation - or to become the lead paper of the Boston-Washington corridor? That, says Mr. Jones , is a complicated question. ''There is no question that the Times has been trying to increase its circulation and its presence within the Northeast corridor,'' he says.