The White House has asked University of the District of Columbia president Lisle C. Carter Jr. to become undersecretary of the newly created U.S. Department of Education, it was learned yesterday.

One source familiar with the selection process said Carter has already accepted the nomination, but a university spokesman denied it.

"All he [Carter] will allow me to say is that he not accepted any position in the Department of Education," said UDC press spokesman Tom Kelly.

Carter, president of UDC for two years, could not be reached directly for comment but Ron Brown, chairman of the university's board of trustees, confirmed that Carter is actively considering the new position. $"I know there has been discussion," Brown said, "and I'm aware that the [White House] offer was made."

As undersecretary of the Education Department, Carter would be the number two official of the new 18,000-employe, $14-billion-a-year super agency that will come into formal being early next year.

Shirley Hufstedler, a federal appeals court judge nominated by President carter in October to head the department, was confirmed for the job last Friday by the Senate and is scheduled to be sworn in today at the White House.

Creation of the Department of Education involes removal of the major educational programs from the president Department of Health, Education and Welfare and combining them with smaller educational elements from other agencies into a single education bureaucracy. HEW is to be renamed the Department of Health and Human Services.

Carter, at 53 a highly regarded leader in the American educational field, was named in the summer of 1977 as the first president of UDC -- the city's public university formed by the merger of Federal City College, Washington Technical Institute and D.C. Teachers College.

Carter was formally installed a year later amid a week-long series of elaborate in augural events costing $68,500, and some city officials privately expressed surprise yesterday that he is now considering leaving after such a short presidency.

"I would hope that he would reject any position that would take him away from his work at the university," Major Marion Barry said through a spokesman late yesterday.

"I think that Lisle has been a good president during the consolidation process, and the board [of trustees] thinks so too," Barry said.

Carter is not a newcomer to high levels in the federal government. He served twice in HEW during the 1960s, once as a deputy assistant secretary from 1961 to 1964, and then as an assistant secretary from 1966 to 1968.

Carter is one of two candidates that the White House has been considering for the undersecretary post at the Department of Education. The other is Samuel Halperin, currently director of the George Washington University Institute for Educational Leadership.

Halperin also has served in high government office before -- as a deputy assistant secretary of health, education and welfare in the Lyndon Johnson administration.

White House consideration of Carter for the undersecretary post comes amid some administration maneuvering to maintain blacks in high visibility positions with the reorganization of HEW and creation of the Education Department.

Many Frances Berry, assistant HEW secretary for education and the highest ranking black in HEW, was passed over for nomination to the new Education Department in favor of Hufstedler, who is white. Several black organizations expressed dismany at this, and Berry announced her resignation, effective Jan. 31.

Black leaders privately theorized that the White House did not want two black women in the cabinet -- Berry and Patricia Roberts Harris, current HEW secretary -- so it nominated Hufstedler to the education job. Carter was then asked to take the number two spot in education as compensation according to the theory.

Several sources said that while the White House approached both Carter and Halperin, who is white, the administration preferred Carter and has simply awaited his decision to accept the nomination. CAPTION: Picture, LISLE C. CARTER JR . . . . has not accepted offer