President Reagan has scheduled peace talks with his eldest son, Michael, to smooth over relations damaged last month in a public squabble between the first lady and the younger Reagan, it was learned today.

The president will also meet his youngest granddaughter, 20-month-old Ashley, for the first time at Friday's meeting at the Century Plaza Hotel, a source close to the Reagan family said.

Michael Reagan, his wife Colleen and their two children will join the president and first lady for the first time since friction erupted when Mrs. Reagan told a columnist that there had been an "estrangement" between Michael and his father over the last three years.

Michael replied on a radio talk show that tension between him and Mrs. Reagan was caused by "jealousy" because he was adopted during Reagan's first marriage to actress Jane Wyman.

Michael Reagan, 39, declined to comment on whether he will meet with the president, who arrived in California today for a week-long New Year's visit.

"I made promises to certain people and I'm going to live up to my promise," the younger Reagan said in a telephone interview from his Los Angeles home.

Last month, Michael Reagan said he wanted to sit down with his father to settle their differences "outside the press . . . so Dad can get on with negotiating with the Russians."

White House spokesman Larry Speakes said today he was not aware of any meeting, but added he "assumed" the president would meet with "some" of his four children during his California vacation.

The source close to the Reagan family said the first family has declined to discuss the meeting at the president's request.

Despite frequent visits to Southern California, the Reagans seldom visit Michael, a businessman and professional powerboat racer.

While the rest of the Reagan family, including daughters Patti and Maureen and son Ron, gathered at the presidential ranch in Santa Barbara, Calif., for the Thanksgiving holiday, Michael celebrated at the home of his in-laws.

In explaining his absence from the Reagan ranch, Michael said at the time, "There's a good reason I wasn't at Thanksgiving dinner. I wasn't on the list."