The National Endowments for the Arts and Humanities both face probable $15 million cutbacks in outlay funds for the current fiscal year, and both agencies have been told by the Office of Management and Budget to prepare for the cuts, according to sources at the NEA and OMB.

The cuts would be part of a government-side package of recisions for the 1981 fiscal year budget that President Reagan is expected to announce soon. Any recisions must be approved by Congress.

OMB public affairs director Edwin Dale said last night that the Endowments were on a list of many government agencies that are candidates for recisions, but that no final decsion had been made by the administration. "Mr. Stockman [OMB director David Stockman] has been preparing a whole bunch of recisions," said Dale. "Once a candidate is on this list, money is held up. Really, it's just to preserve the president's options. I have no way of knowing who President Reagan will choose. The White House will announce a list of recision and deferral messages."

But NEA officials maintain that they have been told by OMB to prepare for the recisions. NEH chairman Joseph Duffey, however, said he has not heard from OMB.

The $15 million figure given the Endowments is in outlay funds, which are the actual amounts of cash that go out to grantees in a fiscal year. Appropriations are the amounts approved by Congress for the agencies. But not all of the appropriated money for one year ends up going out that year. NEA officials estimate $15 million in outlays represents about $30 million in appropriations out of a budget of $159 million. "That's 20 percent of our total budget -- a fair piece of change," said one source.

"We have been told a recision might be possible," said Donald Moore, deputy chairman of the NEA last night. "We're going to have to go through a rather arduous analysis of where all of our monies are. It's a matter of having to freeze the grants process - which we have done."

Moore said the NEA froze grants yesterday or the day before. The NEH froze grants last week temporarily in response to an unrelated action by the Senate Subcommittee on Education, Arts, and Humanities, which recommended cutting NEA current-fiscal-year funds by 6 percent and NEH funds by 7 percent. Ironically, that subcommittee -- in light of revised budget information -- has decided this week to reverse its action. The subcommittee will now offer an amendment -- restoring the funds to the Endowments -- to the full Senate Committee on Labor and Human Resources, according to Glenn Gershaneck, press secretary to the subcommittee chairman.

Recisions in NEA and NEH current-year budgets would be another blow to the Endowments. The Reagan administration budget proposal cut the NEA and NEH budgets for fiscal year 1982 by 50 percent.

For the NEA, according to Moore, "it's a matter of having to go category by category, program by program, and see who's got what. We have to see what grantee has an award letter [from the NEA chairman] already. We can't take that. That's an obligation."