President Reagan today is expected to offer the directorship of the Federal Bureau of Investigation to William S. Sessions, chief judge of the U.S. District Court for the western district of Texas, informed sources said yesterday.

The sources said Sessions, 57, flew here last night from San Antonio and will meet today with the president, Attorney General Edwin Meese III and White House chief of staff Howard H. Baker Jr.

At least two candidates recommended by Meese turned down the job, but Sessions is expected to accept the nomination. He said in a March 17 interview with Texas newspapers that the FBI post would be "the greatest challenge."

Sessions, a Republican, was named a U.S. attorney by President Richard M. Nixon in 1971 and appointed to the federal bench by President Gerald R. Ford in 1974. He gained nationwide attention in 1982-83 by presiding over two trials stemming from the slaying of U.S. District Court Judge John H. Wood Jr., known as "Maximum John" for the tough sentences he imposed on drug dealers.

Sessions imposed two life terms on the convicted killer and sentenced three other defendants involved in the conspiracy to terms of from five to 30 years.

The initial reaction from the FBI, which has been without a director since May 19, when William H. Webster was confirmed as director of the Central Intelligence Agency, was positive. "He's known for his stiff sentences in the Wood case," said one FBI source. "He's a pro-law-and-order person. He's definitely considered a friend of the bureau."

Administration sources also gave a positive assessment of Sessions' chances for confirmation by the Senate. They pointed out that he is strongly backed by former senator John G. Tower (R-Tex.), who first recommended him for U.S. attorney. Sessions also is expected to have the influential support of Sen. Lloyd Bentsen (D-Tex.).

The delay in filling the FBI directorship has frayed relations between the White House and Justice Department. Administration officials said Baker had been pressing Meese to come up with a candidate to fill the vacancy after two early Meese choices, U.S. District Court Judge D. Lowell Jensen of San Francisco and former Pennyslvania governor Richard L. Thornburgh, turned down the job.

Baker reportedly began scouting around for candidates. On Tuesday, Illinois Gov. James R. Thompson (R) urged the president and Baker to nominate Joel Flaum, a U.S. appeals court judge in Chicago. An administration official said the job had been "discussed" with Flaum but that he wasn't interested.

In 1983, The American Lawyer described Sessions as "very formal; always has a court reporter present. Prosecution-oriented. Careful and competent."

Sessions, born in Ft. Smith, Ark., did his undergraduate work and received his law degree from Baylor University. He served in the Air Force from 1951 to 1955. He married Alice J. Lewis in 1952, and they have four children. He was in private law practice for 10 years in Waco, Tex., before moving here in 1969 to become chief of the government operations section of the Justice Department's criminal division.

He lists his hobbies as hiking, climbing and canoeing.

In his March 17 interview, Sessions said he had agreed to be a candidate for the FBI job after being told by Rep. Lamar Smith (R-Tex.) that his name had been forwarded to Reagan for consideration.

"I think it was a difficult decision, especially when you're happy with what you're doing," he said. "It's not an easy thing to do. But I just think it would be the greatest challenge."

Staff writer Ruth Marcus contributed to this report.