President Reagan yesterday made a nationwide radio appeal for a liver donation to an 11-month-old girl who will die in two or three weeks unless she receives a liver transplant.

The president, noting that the success of modern medicine has created a shortage of organs for transplants, also urged Americans to fill out donor cards and leave healthy livers, hearts, eyes, kidneys and lungs to others after they die.

In his unusual presidential plea on behalf of a single person, Reagan said an Air Force jet is ready to transport a donated liver to the University of Minnesota Hospital in Minneapolis where Ashley Bailey, of Clyde, Tex., is awaiting a transplant.

"Right now, somewhere in America," Reagan said, "there might be a pair of stunned and grief-stricken parents whose own baby has died in an accident or is sadly near death. I know if these parents were aware their baby could make it possible for Ashley to live they would have no hesitation in saying: 'Save that little girl.' "

Reagan then asked listeners who knew of possible donors to call the "Living Bank," a Houston center that coordinates organ donations, at 800-528-2971. Within hours, center officials said "several hundred" calls had been received, but none had led to a liver for the child.

In Minneapolis, the girl's mother listened to the broadcast with other family members and said, "We felt like crying--everybody in the room did."

According to the American Liver Foundation, liver disease kills about 50,000 Americans a year. About 75 to 100 liver transplants are performed annually, but a panel sponsored by the National Institutes of Health recently said that the technique has come of age and should be performed more often.

Perhaps the best known liver recipient is Jamie Fiske, who last November received a liver at the same hospital where Ashley Bailey is waiting. Jamie was 11 months old at the time and is doing well.

Reagan said Ashley Bailey's case came to his attention after her congressman, Rep. Charles W. Stenholm (D-Tex.) wrote him about it. The president added that he is aware of other children in need of liver transplants including Candi Thomas, the 11-month-old daughter of a White House electrician.

A senior White House official said later that Reagan, who has twice spoken with Ashley Bailey's parents and written them a letter, is aware that other Americans with sick children may ask the president for help with their problems.

"We want to help people," the official added. "The White House is already dealing with other organ cases, and we realize it is no less important to help them. We're prepared to deal with that."

In his radio speech Reagan said he and his wife, Nancy, had received so many requests from families in need of organ donors that he directed the surgeon general to hold a conference on organ transplants. He said the conference found a need for a program, now under way, to increase awareness of organ donations among hospital officials and "others who need to consider organ donorship when an accident occurs."

"America has faced shortage in the past of everything from nylons during World War II to oil in the 1970s," Reagan said. "But modern medical science has provided us with a new shortage, a shortage of living organs: livers, hearts, lungs, eyes, kidneys. I urge all Americans to fill out donor cards, little cards you carry in your wallet or purse that, in event of death, offer the hope of life to others."