The walls near the Oval Office of the White House have ears - and apparently feet and tails, too.

No one has told the President, and it is not known if he has noticed the patter of little paws in the walls, floors and ceilings in his working area. But the fact is that mice have been seen scampering up the drapes, inching up the electrical cords of the few remaining television sets, and even seen darting across the floors.

Nor is it only the sight and sound of the rodents that have captured observers' attention. Just in time before the arrival this week of Prime Minister Andreotti of Italy, a dead mouse, traced by its smell, was removed from the baseboard air duct is an office near where the President works. Mice enter the ducts through gratings and then scatter to all corners of the mansion.

Actually, the White House apparently has never been without rodents. "The White House traditionally has had difficulty with the little tykes," says a spokeman in the office of the chief usher, although a major renovation of the White House in 1952 did significantly diminish the mouse population for a time.

But some think that subway construction dislodged many of Washington's resident rodents, and a lot of them sought refuge in the White House.

The chief usher's office is charged with controlling the rodents and there are several people on its staff of 100 skilled in carrying out this task. They do so, in fact, on a weekly basis.

White House mice, like other Washington mice, have traditionally been caught in traps. That was until a year or so ago, anyway, when environmentalists claimed that such traps were a cruel way to snuff out lives. Since then, insecticide spray has been used in areas of general concern, but traps are still set in specific areas where mice have been spotted.

Mice were once loved at the White House. President Andrew Johnson's granddaughter had a mouse as pet. Luci Baines Johnson, daughter of President Johnson, had a mouse's first cousin, a hamster. So did Caroline Kennedy, who lost her hamsters to the White House air ducts, causing press secretary Pierre Salinger to interrupt a press conference with news that Caroline's AWOL hamsters had turned up in the President's bathtub, escaped and turned up later in the solarium.

A former White House employee said she was particularly aware of mice after normal business hours when the White House quieted down. "You could hear the patter of little feet above our ceiling," said this person, who worked on the basement level. "It was eerie. It made you cringe."

Even so, the mice have found their way into some people's hearts. Anne Denton Blair, whose book "Arthur the White House Mouse" is based, she says, on a fictional mouse, is working on a sequel. The title: "Where's Rachel?"