John R. Block, a West Point graduate who quit the military to become a successful large-scale farmer and then the top agricultural official in the state of Illinois, is receiving powerful Republican backing to become the next secretary of agriculture.

"He is the kind of man we are looking for -- a producer who does not represent any particular group within agriculture," Sen. Bob Dole (R-Kan.) said the other day.

In other transition developments yesterday, sources close to the Reagan camp said that former Treasury secretary William Simon "got all the votes" when the president-elect's "kitchen cabinet" voted Monday on its preference for secretary of treasury in the new administration. Simon had told friends he would have preferred another job, perhaps secretary of defense, but he appears headed back to the Treasury.

Other sources said Sen. Henry M. Jackson (D-Wash.), rumored as a possible secretary of state or defense, had not made any of the lists of possible Cabinet members that will be delivered to Ronald Reagan later this week.

On Monday, Dole introduced Block, 45, to Republican members of the Senate Agriculture Committee in the office of Sen. Charles H. Percy (D-Ill.). Prior to that, Block had a half-hour private meeting with Sen. Jesse Helms (R-N.C.), who is expected to take over the chairmanship of the committee in January.

Block was appointed director of agriculture for the state of Illinois in 1977 by Gov. James Thompson.

Block's chances were strengthened last week by Dole's statement to reporters that he would "object" to the selection of Clayton Yeutter, who heads Reagan's agricultural advisory panel. Yeutter, a former under secretary of agriculture in the Ford administration and now chairman of the Chicago Mercantile Exchange, had been considered a leading contender because of his Washington experience and his connections to agricultural trade groups.

Dole told reporters that "he [Yeutter] is one of the people I would object to." When pressed to amplify, Dole explained that Yeutter was "not a hands-on farmer" and added that he preferred someone who was "not tied to interest groups in the corporate sector."

A Yeutter associate said yesterday that he was surprised by Dole's remark since Yeutter owns a cattle ranch in Nebraska.

The Mercantile Exchange is one of the nation's largest commodity exchanges, and its members include many major agribusiness companies. Futures contracts are traded there in cattle, hogs, pork bellies, broiler chickens, lumber and potatoes.

The Exchange's political action committee, the Commodity Futures Political Fund, contributed the maximum allowable $5,000 to Dole on July 14 and Oct. 10 this year. The first contribution was allocated to Dole's unsuccessful presidential primary campaign and the second was designated for the general election, even though Dole was not a candidate then. A Dole aide said yesterday that he presumed the money went to pay off campaign debts.

A spokesman at the Exchange said yesterday that Yeutter was "involved in the fund's decision making."

Although Block's duties in Springfield have kept him away from his 3,000-acre corn, soybean and hog farm near Gilson, Ill., farm manager Jim Swise said yesterday that "he still runs it -- he does it all." Swise added that Block seldom comes to the farm except on weekends, but that he still makes decisions on what crops to plant by telephone.

Since resigning from the military after service with the 101st Airborne Division in the early 1960s, Block has expanded the farm from 700 acres to more than four times that size.

Block said this week that he had been approached about taking the agriculture secretary job. He said he had been in touch with Sen. Paul Laxalt (R-Nev.), who heads the Cabinet search team. Percy said he had joined Dole in promoting Block's candidacy.

Others mentioned for the job, in addition to Block and Yeutter, include Richard E. Bell, assistant secretary of agriculture in the Nixon and Ford administrations and now president of Riceland Industries, a rice exporting cooperative in Stuttgart, Ark.; Elton Smith, president of the Michigan Farm Bureau; J. Phil Campbell, a former undersecretary of agriculture, and Jarvis Miller, former president of Texas A&M University.

Several others mentioned but not believed interested in accepting the position are Richard Lyng, who is heading Reagan's agricultural transition team and who has directed the American Meat Institute, which represents major packing companies in Washington, and Minnesota Gov. Albert Quie.

Almost all those in the running for the job, including Block and Yeutter, appear to favor an agricultural policy with a strong emphasis on maximum trade and exports. In his Illinois job, Block promoted food exports and noted that Illinois is the largest exporter of agricultural products in the nation. Swise said that corn and soybeans from Block's farm move into export channels through Illinois and Mississippi River barge facilities.

Yeutter also promoted U.S. trade as deputy special trade representative under Ford.