PITTSBURGH (AP) _ Negotiators for USX Corp. and the United Steelworkers were striving Friday to settle dwindling differences holding up a tentative agreement in a record 169-day work stoppage at the nation's largest steelmaker, sources said.

''Final details on some of the core issues are being worked out,'' one source with access to the top bargainers, speaking confidentially, said Friday afternoon, as negotiators met in Pittsburgh.

''We're pushing it along'' with the intentions of making an announcement later in the day, he said. The mood at the bargaining table was that the two sides were so close to an overall settlement that a breakdown or hang-up was unlikely.

Another source said pay cuts would be around $2 per hour and that the issue of workforce reductions had also been settled.

''They're looking for it to go tonight,'' said another source with close ties to the union hierarchy.

The sources said there was no certainty that the final hurdles could be cleared by Friday night as expected. But while insiders had believed earlier this week that the negotiators were nearing an accord, a settlement this time seemed within reach, they said.

USX spokesman Vic Curtis and USW spokesman Gary Hubbard declined comment on the reports. They said only that progress was being made and that bargaining was continuing for an eighth consecutive day.

Questioned about a report circulating within USX management ranks that the biggest hurdle remaining concerned the company's use of non-union contractors, one source said ''that much is right.''

Another insider said the question revolved around whether curbs on non- union labor would be retroactive or whether the company would be allowed to continue the practice for those jobs already farmed out to contractors.

But when asked about a report that ''three out of four'' key issues had been essentially resolved, one of the sources said ''avoid specifying three out of four'' because progress had been made on many fronts since Jan. 9.

USX had been pressing for contract concessions similar to those the union granted last year to other major steelmakers. One of those competitors, financially troubled LTV Steel Co. of Cleveland, has already won union agreement to reopen the contract due to the company's filing for Chapter 11 bankruptcy reorganization.

The union was willing to yield on wages and benefits, but was fighting hard to make USX fall into line with other big steelmakers who had accepted curbs on the use of cheaper, non-union labor.

Approximately 22,000 union members walked off the job at USX plants across the country on Aug. 1 when their previous contract expired. Another 23,000 steelworkers were on layoff from the company at the time and would be affected by any settlement.

Although USX is the nation's largest steelmaker, its absence has had only minor effects because the markets for most steel products are glutted with low-cost domestic and foreign metal. Market conditions are the prime reason domestic steelmakers have been hemorrhaging cash and demanding worker concessions.

By contrast, the previous record steel walkout, a 116-day strike in 1959, was ended when the U.S. Supreme Court upheld President Eisenhower in citing national security to ordering a return to work by 500,000 union members who had idled virtially all U.S. steel production.