John Linn resigned yesterday as basketball coach at George Mason University and the school announced that it will seek its first full-time head coach.

Two present Division I coaches familiar to the Washington area -- Jack Kvancz of Catholic University and Joe Harrington of Hofstra -- said last night they were interested in pursuing the job Linn, 42, held on a part-time basis for 10 years.

Linn will remain at George Mason as a tenured assistant professor and as coach of the intercollegiate shooting team, which will be advanced to varsity status next season. Linn is one of the best trap shooters in Virginia.

The new basketball coach will be the first full-time intercollegiate coach in any sport at George Mason, which joined the NCAA's Division I two years ago. The basektball team was a surprising 17-8 in its first year of Division I, but fell to 5-21 this season.

Although the budget for the 1980-81 school year has not been formulated, Jay Marsh, assistant athletic director, said basketball will receive significantly more funding than its $105,000 allocation this season.

That broke down to $31,000 for operating expenses, $45,000 for 10 scholarships and $29,000 for salaries, including half of Linn's $19,000 annual salary and the equivalent of two assistants.

Marsh, speaking for Athletic Director Bob Epskamp, who was away because of an illness in his family, said he expects the opeating budget to be doubled, a separate recruiting budget to be established and five additional scholarships to be offered, bringing the Patriots to the NCAA limit of 15.

Donald Mash, vice president for student affairs, said a screening committee chaired by Epskamp will be formed to find a new coach. The process is expected to take at least three weeks.

Mash said, "It will be a while before we'll be able to put on the floor the kind of team other Division I teams are. It would seem we would want someone effective as a recruiter, but also someone who can teach the game of basketball. We need to be respectable with good players."

Mash said the university had no one in mind now for the job. The vacancy will be advertised, Mash said, and "we might surprise ourselves" with who is available.

Among the first to line up were Kvancz, coach the past five years at Catholic, which may decide later this month to drop to Division III, and Harrington, longtime Lefty Driesell aide at Maryland who turned Hofstra from an 8-19 club to 14-14 his first season.

"I told myself if it became available, I owed it to myself and my family to see what it's all about," Kvancz said.

Harrington, who also played at Maryland, said two factors make him interested in the job: his wife, Ann, is an assistant state's attorney in Montgomery County and still lives in their College Park townhouse, and "I love the area."