Michael Dukakis' presidential campaign is conducting public polling to gauge the strength of potential Democratic vice presidential candidates and has requested background information from Jesse Jackson and at least one other contender, sources said Tuesday.

At the same time, sources said Paul Brountas, Dukakis' close friend who is guiding the search for a running mate, received advice in Congress last week to steer clear of Jackson, who finished second in several primaries and caucuses and will have the support of more than 1,100 delegates at the party convention.Several officials said Brountas was advised to balance the ticket with a moderate or conservative Democrat, preferably from the South or West.

"He was told, `You can basically write it off in terms of the election if you pick Jackson," said one member of Congress who attended one of several sessions that Dukakis' adviser held.

Sources, who spoke on condition of anonymity, said that in addition to Jackson, Sen. Bob Graham of Florida has been asked to supply financial and other background information. Sen. Bill Bradley of New Jersey, who also has been mentioned frequently as a possible running mate, has not yet received such a request, his office said.

Brountas met with numerous Democrats during his visit to Washington, including Sen. Ernest Hollings, D-S.C., Jackson's lone supporter in the Senate.

"I provided information about everybody else except me," Hollings said through an aide.

In his meetings with congressional Democrats, Brountas was urged repeatedly to balance the Democratic ticket with someone who can attract votes in the South and West, said several sources, including one congressman who attended a session with him.

"He was advised to select somebody who has broad appeal and to keep himself loose from any commitment for Jesse Jackson at this point," said the congressman, who spoke on condition of anonymity. Brountas' reaction was described as non-committal.

This congressman and others said Brountas also was urged to find a running mate who would bring experience on defense issues and foreign policy to the ticket.

"The focus is on the South and on defense and foreign policy," areas of expertise that are in short supply on Dukakis' resume, said a congressional aide whose boss was one of several Senate and House members to meet with Brountas last week. The sources spoke on condition of anonymity.

Dukakis campaign officials refused to discuss the search for a running mate. "We're in the process of gathering information," said Leslie Dach, the campaign's communications director. Dukakis has said little on the subject, although he has said he wants to make up his mind before the week of the Democratic National Convention.

Relatively few names have been circulating lately as potential running mates for Dukakis, who has wrapped up enough delegates to be assured of a first-ballot nomination at the convention next month. The list includes Sens. John Glenn of Ohio, Sam Nunn of Georgia, Lloyd Bentsen of Texas, Graham and Bradley and Reps. Tom Foley of Washington and Lee Hamilton of Indiana.

Jackson has been mounting a public campaign in hopes of being offered the vice presidential spot, but public polls in a number of states indicate he would hurt the ticket. Thus, Dukakis' aides generally do not believe that the runner-up in the primary season will wind up with the vice presidential nomination.

Nor is a woman deemed likely to join the Democratic ticket. Unlike 1984, when a concerted campaign by Democratic women preceded Geraldine Ferraro's selection as Walter F. Mondale's running mate, there has been no such public clamor this year. And while Brountas met with Sen. Barbara Mikulski of Maryland last week while in Washington, her name has not surfaced as a possible running mate, nor has any other woman member of Congress.

The search for a running mate is beind carried out as quietly as possible, and campaign officials are working to keep the public focus on other issues.

To that end, Dukakis is undertaking an unusually heavy period of post-primary campaign travel in the weeks leading up to the convention, in hopes of generating newspaper and television stories that dwell on something other than the vice presidential search.

And when Brountas visited Congress last week, the campaign insisted that aides be banned from meetings, a request that helps minimize leaks to reporters.

Even so, sources said that in some of the meetings, Dukakis' emissary was urged to look for a moderate or conservative candidate who will be able to attract support in the South and the West, areas of the country where Democrats have run poorly in recent elections.

In addition, he was urged to find a running mate who would provide experience in defense and foreign policy issues that would compensate for Dukakis' relative lack of experience in those areas. Dukakis' only experience in public service has been as a legislator and as governor of Massachusetts.

While little information was available on Dukakis' vice presidential polling, public surveys that are available provide a glimpse of how the selection of a running mate could affect the race.

A survey published in Florida based on interviews conducted in early May reported Bush held a lead of 61 percent to 24 percent over a hypothetical Democratic ticket of Dukakis and Jackson.

When Nunn was listed as Democratic vice presidential candidate in the survey, Bush's margin slipped to 46 percent to 39 percent.

When Nunn was replaced by Florida's home-state Sen. Bob Graham, the Democrats had 46 percent support to 44 percent for Bush.