The Sayings of Mayor Marion Barry are many, but on the subject of the troubles at the University of the District of Columbia they are just one:

"I have some thoughts but no comments."

This singular remark seems to suggest Barry is cogitating about the situation at UDC but prefers to keep his head down while doing so. Why so shy?

Three months after the first reports about questionable expenditures of public funds to support the life style and friends of UDC President Robert L. Green, the mayor might be expected to say something. This is, after all, not just a problem for the university's 15-member board of trustees to work out.

It is also a D.C. government problem. And despite the mayor's best efforts to remain above the fray, the controversy over Green's conduct as UDC president spills over into the District government in some important places.

In the first place, UDC commands a sizable chunk of the city government's financial resources, with over $68 million in D.C. funds budgeted for fiscal 1986. The District has a big stake in what happens at its land-grant university.

In the second, and perhaps more sensitive place, recent developments in the UDC story seem to suggest that the movement of funds and personnel between the university and the city government could prove embarrassing to high officials in the Barry administration and even the mayor himself.

When Green became president of UDC in September 1983, he had the stamp of approval of Barry, who appointed 11 members of the board of trustees that formally hired Green. Green, previously dean of the Michigan State University urban affairs program, is a former mentor of Ivanhoe Donaldson, the mayor's confidant who left city government for an an executive post with the E.F. Hutton company.

Initially, reports of Green's alleged misspending of university funds focused on travel, catering, furnishings and the hiring of friends for lucrative consulting contracts inside the university. In recent weeks, however, several stories have linked Green's associates, supporters and relatives to jobs and consulting contracts outside of UDC -- and inside the District government.

Last week, in response to one of those stories, Barry paid a surprise visit to the D.C. Office of Personnel to inspect the filing system there, according to sources. This brief detour from the usual business of the mayor showed for the first time that while, indeed, Barry may not be commenting about UDC, he is thinking hard about it.

The visit came just days after a report in The Washington Post revealed that the wife of one of Green's chief supporters, UDC Board Chairman Ronald H. Brown, has held a job in the D.C. secretary's office since early 1984. She was hired by Dwight S. Cropp, a Barry appointee who served as secretary before he was named as a UDC vice president the same month Alma Brown started work.

The story referred to notations in personnel form 52B, a confidential document that several District officials said The Post should not have been privy to. The Barry visit was apparently intended to plug any further document leaks.

Ronald Brown, responding to reporters' questions, said last week there was nothing improper about his wife's hiring and that she was not paid with university funds. Cropp asserted there was no relationship between his decision to name Brown to the $43,410-a-year post and his appointment as a UDC vice president.

The Post also reported in the story that Cassandra A. Simmons, a longtime associate of Green from Michigan, had received a $10,000 consulting contract in late 1983 to study the District's international Sister Cities program. This, too, was given by the secretary's office, which is an arm of the Barry administration and is located in the mayor's suite of offices.

Simmons, besides getting the Sister Cities contract and several UDC consulting jobs, also was paid $20,000 for a consulting contract in 1984 with the Public Works Deparment.

Finally, in a story two days ago, The Post reported that Green's niece, Denise Elarms, got an $11,566-a-year job as a clerk in the secretary's office one month after Green took over as UDC president.

To date, then, Green's supporters, friends and relatives have obtained jobs and consulting fees not only at UDC but at two agencies of city government: public works and the secretary's office.

Yet until now, Barry has steered clear of the matter publicly while his legal counsel, Herbert O. Reid Sr., who serves as a UDC trustee, has actively worked in defense of Green.

The spillover of the Green controversy into the District government itself has some wondering whether the UDC story will prove damaging to the Barry administration and whether the mayor eventually will have to weigh in with more than just his thoughts.