The Washington Post Co. is putting Inside Sports magazine up for sale after 18 months of unprofitable operations.

The company announced yesterday that it is "engaged in discussions relating to the sale" of Inside Sports and would continue to publish the monthly magazine until it can be sold.

No asking price or prospective purchaser was identified by The Post Co., which last week sold another subsidiary, The Trenton Times newspapers, to Washington financier Joe L. Allbritton for a reported $10 million or $11 million.

The loss of $4.3 million on the sale of the Trenton newspapers and a television sales operation caused The Post Co. to report on Monday that it lost a total of $440,000 in the latest three-month period.

Industry sources said The Post Co. hopes to get as much as $10 million for Inside Sports. They listed as likely buyers Southwest Media Corp., publisher of rival monthly Sport magazine, Playboy Enterprises and CBS Publications.

Wick Allison, president of Southwest Media, said he had discussed the possible purchase of Inside Sports with Mark Edmiston, president of Newsweek Inc. Allison said the talks were "very preliminary."

"We are not buying Inside Sports," said an official of Playboy. CBS' press representative refused to confirm or deny any interest in the magazine. Peter Derow, who became president of CBS Publications a few months ago, was president of Newsweek when Inside Sports was started in April 1980.

Promising readers a more literate and longer-range view of sporting events than the weekly Sports Illustrated published by Time Inc., Inside Sports scored points for its journalism but struck out commercially.

Bylines like David Halberstam, Studs Terkel, Willie Morris and F. Lee Bailey failed to attract either readers or advertisers in sufficient numbers to produce a profit.

Inside Sports lost $12 million in its first year of operation and continued to lose this year, but at a slower rate. Most of the Inside Sports losses have been absorbed already, and the sale is not expected to have a major impact on the company's future earnings.

Selling the magazine will prove difficult, predicted Chuck Tannen, editor of Folio magazine, which covers the magazine business. "It's going to be tough. I don't think they ever demonstrated there was a market for the magazine."

Last year Inside Sports captured barely 5 percent of the advertising and circulation revenues of sports magazines compared with more than 80 percent for Sports Illustrated, Tannen noted.

After plans to sell the magazine were announced yesterday morning, the price of Post stock climbed 7/8 of a point to $31 1/8 a share, a record high for the stock.

Analyst John Morton of Lynch, Jones & Ryan in Washngton said the new magazine had "developed much slower than anticipated" because Inside Sports had been launched in the midst of "a glut of new magazines."

Any prospective purchaser would have to have "deep pockets and lots of patience," said Morton, who noted that Inside Sports had been unable to reach the circulation level it had guaranteed its advertisers.

Subscription renewals have been running at a high rate, however, and advertising was up sharply in the second year of publication. Inside Sports "has been growing stronger by the month," said Richard Simmons, president of The Post Co.

"It obviously is a magazine with a future. We have concluded, however, that it does not fit into the long-range strategic plans of The Washington Post Co. Accordingly, we reluctantly have decided that it would be best for the magazine--and best serve the company's interest--to sell Inside Sports," Simmons said.