John Neville-Andrews, artistic producer of the Shakespeare Theatre at the Folger since 1981, will resign his position at the end of the current season.

In a letter submitted yesterday to R. Robert Linowes, chairman of the theater's board of trustees, the British-born Neville-Andrews announced his intention to pursue "my other lifelong ambitions," namely independent acting and directing, writing and free-lance producing. Linowes said Neville-Andrews will remain as a consultant through the 1986-87 season.

Although a successor has not been named, sources close to the theater say that Neville-Andrews' replacement is likely to be Michael Kahn, who served for 10 years as the artistic director for the American Shakespeare Theatre in Stratford, Conn., and is currently chairman of the acting department of the Juilliard School in New York.

Kahn confirmed yesterday that he had visited the Shakespeare Theatre last weekend and has had preliminary talks with Linowes, who has spearheaded a campaign over the past year to put the financially imperiled theater on a firm footing.

"I'm very interested," said Kahn. "I've spent a great deal of my life training actors and my interest in classical theater is well known. I've been approached by the Shakespeare Theatre and expressed genuine enthusiasm. But I haven't negotiated or signed a contract yet. If it happens, I'll be very happy to work in Washington. I've done six or seven shows there and feel close to a lot of the people." Linowes said no official announcement of Kahn's appointment would be made until the theater's board of trustees meets on May 5. However, he said, it was "quite reasonable" to expect Kahn to be named to the post.

"I understand John's desire to move on," said Linowes, who also expressed his appreciation for Neville-Andrews' efforts to keep the theater alive during a difficult transition period. But sources said that Linowes and some trustees have been unhappy with the artistic quality of recent shows and believe that the theater cannot expect the substantial financial contributions it needs without an improvement in the quality of its productions.

The Shakespeare Theatre (formerly called the Folger Theatre) was underwritten by the Folger Shakespeare Library until January 1985, when library trustees, citing mounting deficits, announced plans to withdraw financial support and dissolve the company in June. After considerable public protest, the library trustees rescinded the decision and an interim agreement was struck, whereby the library would provide some continuing subsidies for two years.

Linowes was subsequently drafted to head a special committee to explore ways to make the Shakespeare Theatre financially secure after that two-year period. Recently, he said that means raising $600,000 to $700,000 annually, adding, "This theater has to have a national constituency to survive and it has to be good enough to deserve it."

The Shakespeare Theatre appears to have a popular success with its current production of "The Miser," but such recent shows as "The Merry Wives of Windsor" and "The Cherry Orchard" have fared less well critically and at the box office. During his tenure, Neville-Andrews has produced 25 plays for the theater, many of them innovative interpretations of Shakespeare.

Kahn, 45, has directed widely in regional theaters and in New York. Among his productions to play the Kennedy Center are "The White Devil," "Measure for Measure," "Macbeth," "Showboat" and the much-applauded revival of "Cat on a Hot Tin Roof," starring Elizabeth Ashley. He staged 20 classical productions for the American Shakespeare Festival and also served as producing artistic director of the McCarter Theatre in Princeton.

While Linowes and Kahn both said it was premature to discuss any changes in the theater's artistic policies, several longtime members of the resident company were reportedly upset by rumors of Neville-Andrews' impending resignation and were saying they would leave at the end of the season.