Harry R. Hughes, who quit the cabinet of Gov. Marvin Mandel in May complaining that a Mandel friend had attempted to "tamper" with the selection of a management consultant for the Baltimore subway, is going to run for governor in the Democratic primary next year.

Hughes, 50, said yesterday he will campaign on a "clean government theme," saying he has detected "strong sentiment that it's time for a change in Maryland."

When Hughes quit as Maryland's secretary of transportation critics suggested it was the first step in a campaign that would lead to the announcement that Hughes would run for statewide office. But Hughes insisted yesterday that he had arrived at the decision only since his resignation.

Although he has not formally filed as a candidate, Hughes said he has selected a campaign treasurer, Baltimore attorney Lawrence Rodowski, and has discussed with Francis Murnaghan the idea of being campaign chairman. Murnaghan held a similar post in the successful Senate campaign of Paul Sarbanes last year.

The only thing that could prevent his entracne in the race, Hughes said, would be the inability to get needed financial support. But Hughes said he is confident he can get enough money to run what he believes would be a low-budget campaign. He suggested he would need a minimum of $250,000 for the primary campaign, about one-third the figure being mentioned by two announced candidates, acting Gov. Blair Lee III and Attorney General Francis B. Burch.

After Hughs quit in protest of alleged tampering by Victor Frenkil, the head of Baltimore Contractors Inc., and a longtime friend and political ally of Mandel. Frenkil dismissed Hughes' actions with a shrug and the sardonic observation that "he'll make a good governor."

Hughes, who served in the state legislature for 16 years, was Senate majority leader when he was tapped by Mandel in 1971 to head the new state DOT. At the time of his nomination to a cabinet post, Hughes had been mentioned as a possible candidate for the First District congressional seat being vacated by Rogers C. B. Morton, who had been named Secretary of the Interior by President Nixon.

Although Hughes will be one of the candidates running on an anti-Mandel platform, the Eastern Shore native owes much of his early success in politics to the governor.

A native of Denton, Hughes was Mandel's handpicked successor as state Democratic chairman, and worked closely with Mandel when both were in the General Assembly in the 1950s and 1960s.

Hughes also owes part of his early success to Lee who as secretary of state enlisted the support of Montgomery County Democrats behind Hughes as state chairman in 1969.

"I'm convinced that state government can be run without problems, scandal and corruption," Hughes said in an interview. "As the result of so much publicity about corruption in Maryland, it is not enough to eliminate scandal, but we must have an open government so that there is no appearance of corruption either."