The pardon request has been under review for more than a year, the official told CBS Radio News. With the issue still under Justice Department consideration, the White House declines comment on the case.
The Los Angeles Times reports former President Carter has urged President Clinton to pardon Hearst. Officials refused to comment on any contacts between Mr. Clinton and Mr. Carter on a possible pardon.
Mr. Carter commuted Patty Hearst's prison sentence two decades ago.
"She's been a model citizen in every way," Mr. Carter told the paper. "The fact is she deserves the pardon. Her oldest daughter has just entered college. And all this time, Patty has not been able to vote, she's not been a full-fledged American citizen. And I think she's one special case."
The Times said Mr. Carter has had several discussions with Mr. Clinton, Vice President Al Gore and Attorney General Janet Reno.
Patty Hearst Shaw, who now uses her married name, was kidnapped by the radical Symbionese Liberation Army on Feb. 4, 1974, when she was a 19-year-old college student.
Her father, Randolph Hearst, publisher of the San Francisco Examiner, sponsored a food giveaway in an attempt to meet the SLA's demand that he feed the poor in San Francisco. But the group refused to let her go, and she ultimately joined her abductors, assumed the name Tania and denounced her wealthy parents. Two months after the kidnapping, she was photographed carrying a carbine during an SLA holdup of a San Francisco bank.
She was captured by the FBI in 1976 and sentenced to seven years in prison for her part in the robbery. She had served 21 months when Mr. Carter commuted her sentence in January 1979.
Hearst Shaw, now 45, married her former bodyguard, Bernard Shaw, and they live in Fairfield County, Conn., with their daughters, Lydia, 14, and Gillian, 18.
Since her release from prison, she has become a celebrity, appearing in two John Waters movies and several television sitcoms, writing novels and doing charitable work.
She declined comment on Mr. Carter's efforts.
"She wants to express her gratitude for President Carter's confidence in her," her attorney, George Martinez, said. "She is quite moved by his support. He has been her refuge in a sea of misunderstanding."
Mr. Carter's spokeswoman, Carrie Harmon, has confirmed the Times story, but said the former president had no additional comment.
"This is something that President Carter has felt strongly about for a long time and communicated with the Bush administration about as well," Harmon said.