The White House yesterday offered a deal to Democrats on the Senate Finance Committee that could break an impasse over President Reagan's nominations to fill three vacancies on the International Trade Commission.

The White House deal, reported to Finance Committee Chairman Robert J. Dole (R-Kan.) late yesterday, would save the most controversial nominee, Susan Wittenberg Liebler, but the nomination of Washington lawyer Lyn M. Schlitt would be withdrawn. Schlitt had run into some opposition from organized labor because she once represented Honda Motor Co.

The White House, moreover, was reported to have told committee Democrats that it will name "a respectable Democrat" to replace Schlitt, considered by many to be the most competent of the three original nominees.

Hill speculation centered on two staff members: Jeffery Lang, the minority trade counsel of the Finance Committee, a former assistant general counsel of the ITC and someone close to the committee's ranking minority member, Sen. Russell B. Long (D-La.), and David Rohr, staff director of the House Ways and Means subcommittee on trade.

It is unclear whether committee Democrats will buy the deal. But if only a few withdrew their objections, the nominations of Liebler and the third nominee, former Agriculture undersecretary Seeley Lodwick, would be able to go through.

The nine Democrats had been united in their opposition to Liebler, a law professor, who is nominated to a seat that by law must go to a Democrat or independent even though she worked on the Reagan transition team. The Democrats have called her "a closet Republican."

In addition, Liebler has drawn the sharp opposition of Pennsylvania Sen. John Heinz, a key Republican on trade issues, simply because he says he feels she is unqualified.

Although no other Republican has declared his opposition to Liebler, there are reports that Heinz may not be the only Republican opposed to her.

While the commission has assumed new importance as an increasing number of American companies file complaints against foreign competitors, it has operated for nine months with half of its six seats vacant.

According to Senate Republican sources, the White House took its strong stand in support of Liebler because it had promised her she would be named ITC chairman next year. By law, the chairmanship cannot go to the newest member of the commission, and thus the administration wanted all three nominees to be approved at the same time. Liebler would have replaced Alfred Eckes when his two-year term as chairman ends, although he could remain on the commission until 1990.

According to Senate sources, the White House has now pulled back on that promise, which Liebler had acknowledged during her confirmation hearing.

As part of its deal with committee Democrats, Hill sources said, Commissioner Paula Stern, a Democrat, would replace Eckes as chairman. Stern has been considered too liberal by the White House.

Liebler ran into trouble a year ago, when Reagan first submitted her name for a vacant ITC post. Nevertheless, the White House sent her name up again.

In addition to concerns about her real party allegiances, Long charged that Liebler's appointment appeared to be an attempt to get a White House puppet on a commission that is supposed to be independent and quasi-judicial.