Robert H. Tuttle, a White House aide whose father is a member of President Reagan's "kitchen cabinet," has emerged as the leading candidate to become undersecretary of Housing and Urban Development, administration sources say.

Tuttle, a presidential assistant in the White House personnel office, can have the No. 2 job at HUD if he wants it, sources say. But they say Tuttle would forgo the post if he beats out several other candidates to succeed John S. Herrington as White House personnel director. (Herrington has been nominated to be Energy secretary.)

Some officials have questioned Tuttle's ability to manage HUD's day-to-day operations because he has no housing industry experience. He has worked in the auto business and was California chairman of Reagan's 1980 campaign.

Tuttle's father is Holmes Tuttle, a millionaire California car dealer and one of Reagan's earliest backers. Robert Tuttle's wife, Donna F. Tuttle, is undersecretary of commerce for travel and tourism.

The succession question comes at a time when HUD appears to be drifting. The undersecretary's job has been vacant for months since Philip Abrams, a strong manager, returned to the development business. General counsel John J. Knapp has been filling in for Abrams.

Other key officials who recently resigned include Federal Housing Commissioner Maurice L. Barksdale and Robert W. Karpe, president of the Government National Mortgage Corp.

Tuttle was involved in a 1981 controversy when federal bank regulators ordered him to repay a $1.8 million insider loan from a bank partially controlled by his father. Tuttle defended the loan and said the regulators had a "philosophical disagreement to that approach to banking."

Tuttle declined to discuss the HUD job last week. "We just do not comment on personnel actions," he said.

While HUD officials wait for reinforcements, it has become obvious that they have little say in the current budget battles. They issued a report praising rental rehabilitation grants on the same day the Office of Management and Budget proposed to abolish the program. They are trying to save 100,000 experimental housing vouchers from the budget ax, while conceding that they have not issued a single voucher in the year since the program began.

There's been no word on Secretary Samuel R. Pierce Jr.'s appeal to Reagan to spare those programs and urban development action grants, which Pierce has praised. In this case, no news is bad news. CITY VS. CITY . . .

Speaking of UDAG, the department has published regulations that bar cities from using the grants to "pirate" jobs from other cities.

The issue flared up when Jersey City, N.J., won a $40 million urban development action grant for a huge waterfront complex. New York Mayor Edward I. Koch complained that his neighbor was "pillaging and stealing" jobs from across the Hudson River, and Jersey City Mayor Gerald McCann replied that New Yorkers were "making up lies" about his city.

Pierce worked out a compromise in that case, but the new rules, while well-received by New York officials, apply only to future grants. The rules are aimed at the hundreds of applications for speculative office projects that have not lined up corporate tenants.

This could lead to nasty litigation between competing cities and could complicate efforts to rescue the $440 million program on Capitol Hill.