WASHINGTON, November 26--Behind-the-scenes talks looking toward a possible end to the coal strike were widely rumored in the capital tonight as the government pressed for speed in John L. Lewis' contempt of court trial, opening tomorrow.

The air was full of reports of private efforts to get negotiations rolling between Lewis and the mine operators. No official confirmation was forthcoming and some of the principals in the coal picture denied knowledge of such efforts.

However, at Cleveland, Ohio, Cyrus S. Eaton, banker and industrialist, declined to comment on reports that he had exploratory conferences here with Lewis. Lewis and his aides reserved comment on the reports, which indicated that Eaton was interested in using his good offices, if feasible, in helping bring Lewis and the operators together.

Harry M. Moses, president of the H. C. Frick Coke Company, Pittsburgh, a U. S. Steel subsidiary, denied that he had talked with Lewis. There had been reports that he had conferred with the miners' chief on a possible separate settlement for coal mines owned by the steel companies.

Reached in Pittsburgh, Moses said emphatically that he had not even talked with Lewis on the telephone and knew of no conversations by other operators.

The six-day-old strike has already resulted in enforced idleness for about 70,000 workers in industries dependent on coal, in addition to the hundreds of thousands of miners on strike.

Many schools and colleges either were closing down, or planning to do so because of lack of fuel.

The government was depending on the contempt of court case to build up pressure on Lewis and induce him to call off the walkout.

Lewis goes before Federal District Judge T. Alan Goldsborough tomorrow on charges that he committed contempt by refusal to withdraw his notice that the miners' contract with the government ended last Thursday. With the contempt issue out of the way it might take days--the court will consider whether to issue a permanent injunction aimed at ending the walkout.

Justice Department attorneys said they will ask Goldsborough to forego the customary Thanksgiving weekend recess and resume the trial on Friday.