Dallas school superintendent Linus Wright, who has overseen one of the nation's largest school systems during a period of fiscal and racial turmoil, is expected to be nominated as under secretary of education, according to administration sources.

Wright's formal nomination awaits routine background checks, but President Reagan has privately agreed to the choice, the sources said. If approved by the Senate, Wright will become the department No. 2 official, under Education Secretary William J. Bennett. The position has been open since early this year, when Gary Bauer left to become a domestic policy adviser to the president.

Wright, 60, is known as a low-key, back-to-basics administrator who embodies several educational elements promoted by Bennett. In his nine years overseeing the Dallas public schools, he has pushed for greater accountability, instituting teacher tests and a pay plan that ties teacher bonuses to improved test scores. He says he dislikes educational bureaucracies and has allowed parents greater choice among schools by instituting a magnet school plan.

At the same time, however, Wright said he has opposed tuition-tax credits and voucher plans for private-school students. On the subject of prayer in public schools, he said, "I believe in the Supreme Court decisions in separation of church and state."

In a telephone interview yesterday, Wright acknowledged that he is under consideration for the job but said he could not confirm that he has been selected.

He described himself as a political conservative and registered Republican but said he had not been active in politics.

In Dallas, where minority students comprise 80 percent of the public school enrollment, Wright's main challenge has been to implement a 1960 desegregation court order. While his program of magnet schools -- which offer specialized programs to draw students out of segregated neighborhoods -- has been generally well-regarded, Wright also has faced criticism from the minority community.

"I couldn't give him real high marks in terms of moving that integration," said Mary Hepp, an official in the Texas State Teachers Association. "He's an Anglo superintendent. The power base is Anglo, and he leans to the power base."

Mary Rutledge, president of the Dallas school board, said Wright's greatest strength is fiscal management. "We had some really big financial problems," when Wright arrived, she said. "He really did a superb job in getting the district into a really well-respected fiscal position."

The White House had earlier planned to nominate Harvard University professor Glenn C. Loury, a conservative political economist. Loury withdrew his name in early June for personal reasons.

Wright is one of the highest-paid superintendents in the country, earning about $104,000. If confirmed, he will take a pay cut to $82,500.

During his tenure, Wright instituted a controversial plan that based teachers' salary increases on a computer-generated projection of student achievement. The system has been revised, but teacher bonuses still are dependent on improved test scores.