WASHINGTON (AP) _ Attorney General-designate Edwin Meese III wants the Justice Department to pay him $700,000, to cover the legal expenses he incurred during an independent counsel's investigation of his finances, according to a published report.

The Washington Post reported in today's editions that the request has caused problems for Justice Department attorneys reviewing the case of their possible future boss.

The Post, quoting unidentified sources, said some government attorneys believe the request is excessive and want to challenge it before a special three-judge court while others regard it as appropriate.

Following Meese's nomination as attorney general last year, an independent counel was appointed to investigate allegations of financial irregularities.

Jacob A. Stein, the independent counsel, investigated allegations that Meese, as White House counselor, helped secure federal jobs to people who loaned him money.

Stein concluded there was no basis for prosecution, but Meese's nomination to succeed Attorney General William French Smith was put on hold until this year.

Meese's attorney, former Nixon White House Counsel Leonard Garment, declined Friday night to confirm that Meese wanted the government to pay his legal fees of $225 an hour.

''I have nothing to say in the way of comment'' on the request being made to the special panel, which can authorize all or part of the request.

President Reagan has supported legislation to limit fees for lawyers who win cases against the government to $75 an hour.