The Legal Services Corp. has proposed tougher eligibility criteria for poor clients to restrict the number of potential clients and eliminate the practice of advocacy groups hiring legal aid attorneys.

"It will make a difference in concentrating our resources on the poorer people," said John C. Meyer, Legal Services' deputy general counsel. "But this is not really major." Meyer said that the change was prompted largely by the corporation's shrinking budget.

But a spokesman for a liberal advocacy group, who requested anonymity, said that the proposals would hit hard at the long-term unemployed and the elderly, both of whom would tend to have little income but might have assets in the form of home or an automobile.

Meyer said he did not know of the names of any advocacy groups that had used the services of legal aid lawyers. The corporation's press spokesman, Sherrie Bass, said that such records would be kept by the local legal aid offices and not collected in central headquarters.

The proposed eligibility rules would require Legal Services' 336 grant recipients, the local groups that provide federally supported lawyers to the poor, to screen out prospective clients with equity of more than $15,000 in a home or $4,500 in a car, unless the applicant had substantial debts or medical expenses.

No services would be provided anyone whose income is more than 187.5 percent of the national poverty level, $9,862 for a family of four.

But services could be denied at income levels well below that. According to the proposals, assets "must" be considered in the case of an applicant whose income is 125 percent or more of the poverty level, although mitigating factors, such as medical expenses, "may" be considered.

There are also sections requiring assessment of a prospective client's future income outlook. The advocacy group spokesman condemned those sections as vague and too broad.

The new rules also would require local legal aid organizations to establish the eligibility of members of a client group, and of the group as a whole, before agreeing to represent the group. "Even a group composed primarily of eligible clients may have some rich members or may have significant sources of funds other than from its membership," Legal Services' notice said.

Legal Services, which became a thorn in the side of many local and state governments in the process of developing a reputation for being a feisty advocate of the poor, has been targeted for abolishment by the Reagan administration.

Its current budget is $241 million, down from $321 million in fiscal 1981. It has requested $257 million for fiscal 1984, a figure used in Senate versions of the continuing resolution. House bills include a $296 million figure.

According to the corporation's press office, the number of attorneys working for Legal Services grantees, such as the well-known California Rural Legal Assistance program, has dropped from 6,337 in fiscal 1981 to 4,793 last Oct. 1.

"We're interested in people's rights to an attorney," Meyer said. "We don't judge the merits of the cases brought. We're not in that business. We never were in that business legally, though we used to be in it more than we are now."