Attorney General Edwin Meese's wife, Ursula, will undergo questioning shortly in the criminal investigation of her husband about her own $40,000-a-year job, say sources familiar with the case.

The office of independent counsel James McKay is trying to determine whether longtime Meese friend E. Robert Wallach in effect helped supplement the Meeses' income by recommending Mrs. Meese for jobs, said sources familiar with the probe, speaking on condition of anonymity.Mrs. Meese has retained the same Washington law firm representing her husband, said James Rocap, one of Meese's lawyers. She will either make a federal grand jury appearance or be questioned by investigators from McKay's office.

McKay said last week that his investigation of Meese, also encompassing an examination of the circumstances surrounding Mrs. Meese's job, would continue at least until the end of April.

McKay last month subpoenaed records relating to Mrs. Meese's post with the Washington chapter of the Multiple Sclerosis Society, said a lawyer for the chapter, James Bierbower.

A lawyer for Wallach, George Walker, has told The Washington Post that Wallach had suggested Mrs. Meese for a job with a local radio station owned by the Bender family of Washington.

Mrs. Meese took the position with the MS Society instead. However, Bierbower said the Bender Foundation of Washington, controlled by the same family that owns the radio station, is contributing the $40,000 a year that constitutes Mrs. Meese's salary with the MS group.

Calls to the Bender Foundation seeking its reasons for paying Mrs. Meese's salary were not returned.

Mrs. Meese has been a volunteer for the MS Society since 1981 and for the past two years has been in charge of a program called Operation Job Match, matching MS victims with employers.

Mrs. Meese also was questioned in an earlier independent counsel's investigation of Meese in 1984. In that investigation, independent counsel Jacob Stein probed Meese's failure to include in his financial disclosure statements a $15,000 loan by Edwin Thomas to Mrs. Meese. Thomas later became Meese's assistant counselor at the White House. The independent counsel found no connection between the loan and federal jobs obtained by Thomas, his wife and his son.

In another development Monday, Justice Department sources said Meese will face

an ethics investigation by his own department's Office of Professional Responsibility if McKay doesn't seek an indictment. Such an inquiry ultimately could lead to a recommendation to President Reagan that Meese be fired.

Former Assistant Attorney General William Weld's files on the attorney general's dealings with Wallach were moved to OPR last Friday, the sources said.

Material collected by Weld's criminal division last year led to McKay's criminal investigation of Meese.

McKay said Friday he has insufficient evidence to date to warrant seeking an indictment of Meese in connection with his involvement with a $1 billion Iraqi oil pipeline touted by Wallach or his involvement with the regional Bell telephone companies at a time when he held $14,000 in Baby Bell stock. In December, McKay said he didn't have sufficient evidence at that time to warrant seeking an indictment of Meese in connection with his assistance to scandal-plagued Wedtech Corp.

McKay said that if he decides not to seek a criminal indictment of Meese, the independent counsel's office "will refer all of those matters for review and action by the appropriate administrative authorities," a reference to OPR.

OPR's chief, Michael Shaheen, denied assertions by Justice Department sources, speaking on condition of anonymity, that his office had begun examining Meese's ties to longtime friend Wallach last year.

That review was halted when McKay launched his criminal investigation of Meese last May 11, the sources said.