The Minneapolis Star apparently is about to join the rapidly growing list of defunct afternoon newspapers in the nation's big cities.

Reports circulated in the Twin Cities yesterday that the Star, which has been losing money and circulation for several years, will publish its last editions on April 2 and will be merged the following week into the morning Minneapolis Tribune. Both are published by the Star and Tribune Co., headed by John Cowles Jr.

Donald R. Dwight, publisher of both papers, declined to comment on the persistent reports, saying he had "adopted this position in the past 24 hours" because his denials did not stop the rumors.

The Tribune carried a story yesterday quoting Dwight and other executives as saying they would not respond to reports on local television stations and in the St. Paul papers because it was futile to do so.

Reporters at the Minneapolis papers, however, said they expect the announcement to be made today at staff meetings and in a press conference. They said 68 of the 299 newsroom employes of the Star probably will be let go after the merger with the Tribune. More than 100 employes of both papers already have accepted offers of early retirement.

Stephen D. Isaacs, who in four years as editor of the Star has been unable to find a formula to halt the paper's rapid erosion, apparently will not have a place in the merged operation. He was said officially to be on vacation outside Minnesota yesterday. Dwight said, "Steve was, and remains, the editor of the Star," but employes of the paper said his office has been cleaned out.

If the Star does fold, it will be the fourth major afternoon paper to go under in the past nine months, following The Washington Star, the evening edition of the New York Daily News, and the Philadelphia Bulletin, which died in January.

The Minneapolis Star, founded in 1920, was at one time the leading newspaper in the Twin Cities, with a daily circulation of about 300,000, but by the end of 1981 its readership had plummeted to about 170,000. The parent company has made no secret of its overall financial distress, and suffered a setback last week when stockholders of the Des Moines Register and Tribune, headed by another branch of the Cowles family, decided against merging the two operations.