Attorney General-designate Edwin Meese III is seeking about $700,000 from the government to pay legal bills incurred in his defense in an independent-counsel probe last year, and the request has become a problem for the Justice Department, which he has been chosen to head, sources confirmed yesterday.

Some department officials said they regard the request as excessive and want to challenge it before a special three-judge federal court that oversees matters involving the Ethics in Government Act. Other department officials said it is appropriate.

Officials on both sides acknowledged that it is embarrassing and awkward even to consider payments to someone who is nominated as their boss.

Reagan administration policy has been that lawyers who win cases against the government are entitled to fees of no more than $75 an hour. President Reagan has supported legislation to set that limit.

Lawyers who successfully defended Meese during a six-month investigation by independent counsel Jacob A. Stein are seeking as much as $225 an hour, according to informed sources. The judicial panel may authorize all or part of it.

Meese's team, headed by former Nixon White House counsel Leonard Garment and San Francisco attorney E. Bob Wallach, defended him against a broad range of allegations, including some that he gave federal jobs to people with whom he had financial relationships.

Garment's request, according to sources, includes fees for his time, for four senior associates at his firm, four or five paralegals, law clerks, accountants and other support staff for six months.

All documents in the matter are under court seal.

Sources said Garment usually bills clients about $225 an hour, a standard rate for a senior partner at a top-level Washington law firm. Sources said that is approximately what he charged Meese.

Stein, who reportedly has filed a response for the panel to Meese's request, declined to comment yesterday. His response is also under seal. The Justice Department, whose response was due last week, asked for an extension.

Stein apparently noted that the law says the court could "reimburse" persons cleared by an independent counsel, other sources said. That might mean that Meese must pay his lawyers and then collect from the court, according to lawyers familiar with the act.

Attempts to elicit comment from Meese were referred to Garment.

"The application, for technical reasons, was made by Mr. Meese," Garment said yesterday. "But, in fact, the matter is between the attorneys and the court. We've filed detailed affidavits to support our charges to Mr. Meese. The court will decide whether and to what extent our fees and expenses should be allowed."

Garment said he expects the court to unseal the documents and said, "At this time, we have no comment to make on the details . . . . "

Another attorney said Meese's lawyers believed that they might be required to charge Meese their standard rates lest any deduction be viewed as a favor to Meese, precisely what Stein investigated.

A Justice Department spokesman said yesterday that Stein, his five lawyers and support staff were paid $320,000 for the investigation, not including the cost of using four Federal Bureau of Investigation agents. In addition, the independent counsel and his staff's salaries are set by law at no more than about $70,000. No similar law applies to the defense.

This is the first time a government official has cited a 1983 amendment to the law allowing reimbursement for attorney fees in independent-counsel investigations. Government officials previously had to pay their lawyers.

Federal law requires the government to pay "reasonable" attorney fees to anyone who wins civil-rights suits against the government. The 1983 amendment, however, leaves the matter to the special court.