After an eight-month federal investigation, Rep. Frederick W. Richmond (D-N.Y.) is expected to be indicted this week, possibly as early as today, according to sources familiar with the probe.

Justice Department sources refused yesterday to say what the charges will be. Edward R. Korman, the U.S. attorney in Brooklyn, has been working on the investigation since the first of the year and is believed to have obtained Justice Department approval for the indictment. Korman did not return telephone calls, but a grand jury is known to have been focusing on several allegations, including:

* Whether Richmond knowingly used his influence to obtain a job on the House payroll for an escaped prisoner from Massachusetts,

Whether Richmond or his campaign aides violated federal election laws by using employes of the Walco National Corp., of which Richmond is a director and major stockholder, in his 1978 and 1980 elections

* Whether the multimillionaire congressman had aides purchase illegal drugs for his use.

Michael Kahan, press secretary in Richmond's Brooklyn office, said yesterday that Richmond has received no notification that an indictment is imminent.

"We know they've been seeking indictments for months and months," he said.

"I'm not saying it won't change, but at the moment there's nothing going on that hasn't been going on for months."

Richmond has been campaigning for a fifth term in Congress and filed papers on the Tuesday deadline for the Democratic primary.

Four years ago Richmond was charged with one count of sexual solicitation after a 1977 incident involving a boy who complained to his parents that Richmond had made sexual overtures when the boy delivered groceries to the congressman's Washington home.

Months later, an undercover District policeman carrying a concealed tape recorder claimed that Richmond made similar overtures to him.

After the indictment, Richmond acknowledged he "had made solicitations with the payment of money" to two males.

The charges were dropped after he agreed to seek counseling. Afterward, Richmond won renomination and was elected with 77 percent of the vote.

Much of the current investigation has focused on Earl W. Randolph Jr., a long-time acquaintance of Richmond.

Randolph escaped in July, 1980, from a Massachusetts halfway house, where he was being held on an 18-year sentence for assault with intent to kill. Six months later, with Richmond's recommendation, Randolph went on the House payroll under the assumed name of John McLoughlin.

Randolph, using the assumed name, was arrested March 25, 1981, in New York City for male prostitution after he allegedly solicited an undercover policeman, suggesting a sexual act in the back seat of a car that belonged to Richmond.

A major question before the grand jury was whether Richmond knew Randolph was a fugitive when he helped him get the House job.

A federal judge in New York ruled in June that letters to and from Richmond concerning Randolph must be turned over to the grand jury. Richmond's lawyers had claimed that the letters were personal and that giving them to the grand jury would violate Richmond's privilege against self-incrimination.