State Sen. Stewart Bainum Jr., a wealthy Montgomery County Democrat, says he is seriously considering a race for the U.S. Senate seat held by Republican Charles McC. Mathias Jr.

Bainum, 39, has hired the firm run by national Democratic pollster Patrick Caddell to conduct a survey assessing his chances against a field that is expected to include Gov. Harry Hughes, according to Montgomery County political sources.

Bainum, nearing the end of his first term in the Maryland Senate, declined to comment on the reports he has hired Caddell, but said he is "doing some research on my political options," including a possible bid to capture the Democratic nomination for U.S. Senate.

"I'm taking a look at a number of different options," said Bainum. "The Senate is one of the races, but that is not the only option I am looking at. I've enjoyed my seven years in the legislature, but at some point I'd like to move on."

Bainum said he would make a decision on a Senate race within a few weeks.

If Bainum does seek the Democratic nomination for U.S. Senate, his candidacy could add an uncertain element to a contest in which Hughes would be considered the favorite. Although the two-term governor has said he has not yet made a decision on the race, many Democratic politicians expect him to run.

U.S. Rep. Barbara A. Mikulski is also considering joining the race, and recently conducted her own poll.

Mathias has not yet announced whether he will seek reelection.

"The Senate is one you have to consider if you are going to make a move next year," said Bainum. "It's a major political office that is up for grabs. You'd have to wait six more years before it is up for grabs again."

Bainum, who served one term in the House of Delegates before capturing his Senate seat, said he is has also been urged to run for Montgomery County executive.

Although Bainum probably suffers from low name recognition outside the Washington area, he has the personal resources to mount a statewide campaign. Among the questions asked in the Caddell poll, according to one source, is how voters would feel about a candidate who spent $1 million of his own money.

Bainum is no stranger to somewhat quixotic bids for higher office fueled by his own funds, which come from his family's nursing home and motel interests. In 1981 Bainum ran in the special election to fill the 5th District congressional seat, spending about $50,000 of his own money but finishing well behind winner Steny Hoyer.

One longtime Democratic activist in Montgomery County speculated that Bainum might mount a long-shot effort for the U.S. Senate to build name recognition for a future race.

"That's what he did with Hoyer," said the source, who asked not to be named. "He knew he couldn't beat Hoyer, but he got enough name recognition to win the state Senate seat."

"I don't think he can beat anybody" in the U.S. Senate race, said the activist, "but he can do himself a lot of good by being the issue-oriented thoughtful young man."

Many Democrats, among them Hoyer, said that Hughes should be given an unobstructed field in the Senate race to maximize the party's chances of wresting the seat from Mathias, who is completing his third term. A well-financed effort by Bainum could divert Hughes' money and effort and leave him weakened for the general election that follows the September 1986 primary by only six weeks.