White House chief of staff James A. Baker III has asked for a report on allegations that Warren Richardson, the administration's choice to be an assistant secretary of health and human services, is anti-Semitic, deputy press secretary Larry Speakes said yesterday.

The charge was made by Rep. Samuel Gejendson (D-Conn). on the basis of an article Richardson wrote for The New York Times in 1971 and his four years as general counsel of the Liberty Lobby.

Richardson has denied the allegation.

President Reagan met with Cardinal Terrence Cook yesterday as the president was reported feeling better every day at the end of his first week back in the White House following the attempt on his life March 30.

Cooke, the Roman Catholic archbishop of New York, said he and Reagan discussed "the great hopes of peace in this world" during a 35-minute visit in the family quarters of the White House.

The presient also met with his top three advisers and with Ken Khachigian, his chief speechwriter.

Speakes siad that Reagan and Khachigian discussed a series of speeches and messages that the president plans to deliver, including an economic address aimed at boosting the chances of winning congressional approval for his economic recovery program. No date has been set for that speech, but April 30 is considered the most likely day.

The president walked outdoors yesterday for the first time since he was wounded. He and Mrs. Reagan took a short walk in the garden outside the Oval Office.

He is expected to increase his workload gradually next week, but Speakes said there was no definite plan for Reagan to return to working in the Oval Office. The president has been spending about two hours a day on work since his release from George Washington University Hospital.

Speakes also said that a few days after the assassination attempt the president received a telegram "expressing regret" from John W. Hinckley Sr., the father of the man accused of shooting Reagan and three other men.

Meanwhile, the White House announced that Reagan's first trip away from Washington since being shot will occur May 17 when he flies to South Bend, Ind., to deliver the commencement address at Notre Dame University.

Reagan also intends to give the commencement speech at the U.S. Military Academy at West Point, N.Y., on May 27, Speakes said.