Baltimore Mayor William Donald Schaefer, who is seeking the Democratic nomination for governor, has asked state Senate President Melvin A. Steinberg to be his running mate, and Steinberg is expected to accept the offer, sources said today.

The official announcement of the Schaefer-Steinberg ticket will come early next week, according to the sources, who described the arrangement as "90 to 95 percent sealed." The reluctance of Steinberg's family was said to be the only impediment to his running for lieutenant governor.

Steinberg said today he and the mayor have "had conversations and discussions" about what role he might play as lieutenant governor but that he will make no final decision until he consults with his family and fellow senators.

Mark Wasserman, Schaefer's campaign manager, refused to discuss the reports.

Steinberg, 52, has represented the Pikesville area of Baltimore County in the Senate for 20 years, the last four as president of the 47-member body. A master of legislative give and take, Steinberg has earned a reputation as an extraordinarily effective president who has repeatedly succeeded in imposing his will on the often unruly Senate.

Because of that role, Steinberg is viewed as someone who could ably serve a Schaefer administration in its relations with the General Assembly.

Some of Schaefer's supporters believe that Steinberg, who is Jewish, would boost the mayor's support among some moderate and conservative Jewish voters who are said to be concerned over the choice of a running mate by the mayor's opponent, Attorney General Stephen H. Sachs. Sachs, who also is Jewish, is running with retiring U.S. Rep. Parren J. Mitchell, a black who began his congressional career by defeating a Jewish incumbent in 1970.

They also said Steinberg would help solidify the mayor's already strong appeal in Baltimore County, which traditionally delivers the second highest vote after the city of Baltimore during Democratic primaries, and would open doors elsewhere because of his close relationships with his fellow senators.

But other observers, including some of Schaefer's supporters, suggested that the mayor, who is leading Sachs 2 to 1 in state polls, is already running well among those constituencies and that the selection would bring little political advantage.

Baltimore City Council member Rikki Spector said, "My people think the mayor's Jewish, so that Steinberg wouldn't make any difference."

One Baltimore politician sympathetic to Schaefer's candidacy, who asked not to be identified, also said Steinberg would serve as a "battle cry among teachers," whose largest union has already endorsed Sachs and who view the Senate president as the prime villain in passing controversial legislation in 1984 reducing public employe pension benefits.

Sachs partisans, characterizing Steinberg as an old-school, Baltimore area politician, said the choice would highlight the contrast between Schaefer and the attorney general, who projects himself as a liberal reformer.

"If you sniff real hard you can detect the smell of the clubhouse left over from 20 years ago," said state Del. Timothy F. Maloney (D-Prince George's). "It's the same aroma."

Some Montgomery County politicians who support Schaefer also said the choice would not help, and might hurt, the mayor's ticket in their county. "It does him harm in Montgomery County," said one. "Nobody knows Mickey and it reinforces the Baltimore political image."

Other Schaefer supporters said the choice may help them in Prince George's County because of the perception that the leader of that county's Senate delegation, Thomas V. Mike Miller Jr., would be the natural successor to Steinberg as Senate president.