President Reagan plans to nominate Frank S.M. Hodsoll, deputy assistant to the president and deputy to White House chief of staff James Baker, for the chairmanship of the National Endowment for the Arts, according to White House and congressional sources.

The White House may wait until the end of this month or the beginning of next month to announce both Hodsoll's nomination and that of the new chairman of the National Endowment for the Humanities, according to a White House source. The White House has not yet selected a nominee for chairman of the NEH, but supposedly two lists of possible names are circulating. They include men and women, academics and nonacademics. Among the candidates are William Schaefer, executive vice chancellor of UCLA; William Bennett, director of the National Humanities Center in Chapel Hill, N.C.; and Melvin E. Bradford, professor of English at the University of Dallas and one of the members of Reagan's transition team for the NEH.

White House sources say the announcement of the new chairmen might be made at the same time the president receives the report of the Presidential Task Force on the Arts and the Humanities, the group that has been examining ways to improve private funding for the arts.

Hodsoll, 43, helped organize the task force on the arts and the humanities. He is a lawyer who has held various civil-service positions in the Nixon, Ford and Carter administrations. He has worked in the Foreign Service, environmental agencies, the Commerce Department and the State Department. He worked for Baker when Baker was the assistant secretary of commerce in 1974. At State, Hodsoll was deputy to the president's special representative for nonproliferation.

However, he has held no job in the area of arts administration. Livingston Biddle, the current NEA chairman appointed by Carter, was a special assistant to Sen. Claiborne Pell (D-R.I.), and both were involved in writing the legislation founding the arts and humanities endowments.

"I don't think anyone would say Mr. Hodsoll is not up to the job," said Polly Gault, staff director for Sen. Robert Stafford's (R-Vt.) subcommittee on education, arts and humanities, which will be involved in the hearings on the nomination. The full Senate Committee on Labor and Human Resources will hold the hearings. Gault said that to the best of her knowledge the nominee will be Hodsoll. "I think the chairman of the endowment has to know the people he'll have to deal with," Gault said. "It depends on the individual. We understand Hodsoll is a hard worker and very enthusiastic."

Hodsoll, who declined to confirm that he would be nominated, was involved in arts as an undergraduate at Yale. He did work in theater and he helped arrange a series of Carnegie Hall concerts by northeastern college singing groups.

Although Hodsoll has no experience in arts administration, the fact that he has been well-connected in the White House could be an asset in chairing the endowment.

Sen. Pell, one of the spearheads of the legislation founding the endowments, said of Hodsoll, "I know him and I like him. He has excellent administrative abilities. People would say I'm subjective about this, but I hope he continues to run the endowment as efficiently as Biddle has done . . . Naturally it would be helpful if he had arts experience, but he will have people working for him who have arts experience. I think he has wide-ranging judgment with a basic sympathy for the arts."

"If he is nominated, I would predict the hearings will be lively," said Gault. "I think the senators will be interested in discussing the task-force report. But we're not expecting any problems."