Under pressure from Sen. Bob Dole (R-Kan.), the Reagan administration has reportedly agreed to soften some of its proposed food stamp cuts, though the program would still face sharp reductions, administration and Capitol Hill sources said yesterday.

Dole, a longtime friend of the food stamp program, which benefits agricultural interests as well as the poor, has now become a major power in the Senate. As chairman of the Senate Finance Committee, he is keeper of the gate for all the major tax, Social Security, welfare, Medicare and Medicaid changes that President Reagan hopes to push through Congress. Anyone with that much power has influence over virtually anything, even if it doesn't fall directly in his jurisdiction.

But Dole is also chairman of the Senate Agriculture nutrition subcommittee, which has jurisdiction over the food stamp program. It was in this role that he recently began inquiring into how much the poor would be hurt by Office of Management and Budget Director David A. Stockman's proposal to cut food stamp outlays by $2.6 billion. These outlays had been projected to total $12.7 billion in fiscal 1982.

According to admnistration sources, Dole called Stockman several times and also met with him late last week and negotiated a cutback in the reduction plan. At a meeting with Dole and others, Stockman reportedly indicated that instead of $2.6 billion -- which Dole's choice as Secretary of Agriculture John A. Block had supported -- the proposed slash in food stamps would be only $1.5 billion to $1.8 billion.

Dole's apparent success in reducing the cutback could create some sparks at the Senate Agriculture Committee whose new chairman, Jesse Helms (N.C.), has been one of the most voluble critics of food stamps.

Helms was not commenting about the matter yesterday, and aides said that the senator's position on budget cuts is unchanged: Congress will have the last say on any cuts or major changes in program.

House Democrats, meanwhile, still in the majority in their chamber, seem ready for all-out battle over food stamp reductions."It doesn't make a big rat's --- what they do downtown . . . . If they go higher on the cuts we'll simply have more amendments to restore the money," a House Agriculture Committee is prepared to have not more than $1 billion in food stamp cuts."

According to sources, Stockman indicated he would alter two proposed eligibility changes. One, included in Stockman's "black book" of proposed cuts, would have reduced benefits by 35 cents' worth of stamps for each dollar earned by a recipient, instead of the current 30 cents. Stockman said he would drop this change, sources said.

He also decided to recommend that a recipient cease to be eligible for the program when his gross income reaches 130 percent of the poverty line, sources said. This is a lower figure than applies in practice now in many cases, but somewhat higher than Stockman had originally contemplated.

Meanwhile, several large coalitions began mobilizing to oppose the cuts in food stamps and a proposed $1 billion cut in school lunches and child feeding.

One, called the National Child Nutrition Coalition, consists of about 30 organizations and has as its primary purpose to fight the school lunch cuts. It includes the American School Food Service Association; the Food Research and Action Committee (FRAC); the National Farmers Union; the Children's Foundation; National Milk Producers Federation; and American Federation of State, County and Munincipal Employes.

Another, fighting food stamp cuts, has many of the same groups plus the United Auto Workers, United Food and Commericial Workers and National Urban League.