President Reagan will become deeply involved in shaping the 1983 budget next month and will personally hear his Cabinet officers' appeals of proposed budget cuts, deputy White House press secretary Larry Speakes said today.

Speakes said the president "expects an unusual number of appeals" because the cuts for 1983 will be "very deep." These are not reductions from the 1982 level of spending, but are cuts in the rate of growth of federal spending, he added.

Reagan, who will return to Washington Monday, will begin his personal involvement in the budget process at a luncheon next Friday, Speakes said. During a two-week period in mid-December, the president is scheduled to attend nine sessions of approximately two hours each. The bulk of this time will be spent considering appeals by heads of departments and agencies against budget cuts recommended by David A. Stockman, director of the Office of Management and Budget.

The 1983 budget must be submitted to Congress in January.

Reagan's personal participation in budget meetings will coincide with the next deadline for keeping the federal government in spending money.

Last Monday, Reagan vetoed a resolution that would have kept federal spending at a level he considers too high. Instead, he ordered nonessential government services to shut down. But he agreed with the Congress on a temporary truce that set Dec. 15 as the new deadline for a decision on the level of spending.

Speakes has said that the days until Dec. 15 are not a time for negotiations. The president does not want to make further compromises. Reagan still wants roughly $8 billion in cuts that he proposed Sept. 24, but has said he is willing to accept roughly half that amount. However, Congress offered him only $1.5 billion in reductions last Monday, and he cast his first veto.

According to Speakes, OMB made the "initial mark" on the 1983 budget some weeks ago and sent initial proposed budget levels to the departments and agencies, which then had about 72 hours to review the numbers and appeal to OMB.

OMB officials then spent roughly 24 hours considering these appeals before making what is called the "director's mark"--in effect, Stockman's final word--and sending totals back to each department.

"This is the standard calendar budget procedure. We are on target," Speakes said.

The meetings with Reagan will be a final appeal opportunity. In addition to the president, presidential counselor Edwin Meese III, chief of staff James A. Baker III and Stockman will participate in weighing the appeals, Speakes said.

Baker, Stockman and presidential aide Richard Darman are the principal White House representatives working with Congress in an attempt to avoid a new confrontation on current spending that might lead to another temporary curtailment of government activity on Dec. 15.

Speakes said that the nine sessions Reagan will attend will consider what to do about the so-called entitlements programs, under which the government provides cash benefits to citizens. These programs are a massive expense, but one that is politically difficult to reduce--as Reagan discovered last May when he proposed some cuts in Social Security. He withdrew them in the face of strong political opposition.

The budget sessions also will cover possible tax increases. Stockman is known to think that raising revenues by new or increased taxes other than income taxes is necessary to control budget deficits. Reagan has resisted all but small tax increases.