Senate Republicans, despite public denials of any firm deals with the White House, continued to search yesterday for face-saving ways to give President Reagan his three-year package of budget reductions without more painful spending cuts this year.

The denials from Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) and Office of Management and Budget Director David A. Stockman came in the face of continued "not for attribution" reports from informed sources that the White House has signaled willingness to go along with substantial modification of the Reagan budget plan.

It was termed a "pretty good understanding" by one source, and Baker issued a clarification of his earlier denial late yesterday. "There are no final arrangements yet," said Baker, "but we are working toward a package, and we intend to bring up appropriations bills on the floor of the Senate beginning this week."

Senate Appropriations Committee Chairman Mark O. Hatfield (R-Ore.) has insisted that his committee can approve no more than $5 billion to $6 billion in appropriations cuts --about half the $10.4 billion that President Reagan proposed last month in an overall package of $16 billion in spending cuts and new revenues.

Informed sources said Sunday that top White House officials have agreed to the $5 billion to $6 billion in appropriations cuts, along with $7 billion to $8 billion in revenue increases, as a compromise package. The report was followed yesterday by a rash of denials, quasi-denials, and claims of noninvolvement.

One of the same sources said yesterday that the denials were prompted largely by concern that any such agreement might appear to be a retreat on the part of the White House, even though the eventual package would still give Reagan the more than $100 billion in additional budget savings that he wants by 1984.

The sources also said that no agreement could be considered final until it had the agreement of other Republican lawmakers besides Baker.

Reports of the agreement were published in yesterday's editions of The Washington Post and the New York Times.