MADISON, Wis. (AP) _ State leaders are trying to make Wisconsin less attractive to poor people considering moving there by offering new residents only as much in welfare as they would have received in their old state.

Following a recent study that concluded the state was a ''welfare magnet,'' Gov. Tommy G. Thompson is proposing to limit payments for incoming welfare recipients for their first three or six months in Wisconsin, his aides said Friday.

The Republican governor's plan, to be included in his budget message to the Legislature later this month, was revealed a day after a key Democrat, state Senate Majority Leader Joseph Strohl, advocated a similar plan.

''It is time that we Democrats admit that people really are moving here because of our higher benefits, and begin to address it,'' Strohl said.

But others say the two-tiered benefit plan, even if it applies only during a resident's first few months in the state, is unconstitutional.

''The Supreme Court says it's illegal to have a two-tiered system of benefits,'' said the Rev. Ted Steege, head of the Lutheran Office of Public Policy in Wisconsin.

Steege said each state ''has established a standard of need for welfare recipients, and no state can create a new class of citizens who aren't entitled to that.''

The Supreme Court in 1969 ruled a one-year waiting period for Aid to Families with Dependent Children benefits in several states and the District of Columbia was unconstitional because it created ''an invidious distinction'' among citizens.

But lawmakers here said a two-tiered plan - in effect, giving out lower benefits, rather than no benefits, for the first few months of residence - has never gone before the court.

Strohl said he was ''mildly optimistic'' the courts would uphold such a plan because it does not deny all benefits based on one's leNg h of residency in the state.

A recent report from the Wisconsin Policy Research Institute that found 29 percent of new welfare cases in Wisconsin were people from other states.

More than one-fourth of the new arrivals were from Illinois, where a family of three receives $558 a month in AFDC benefits and food stamps. A family of three received a total off $542 a month in Indiana. Combined benefits for such a family in Wisconsin are $680 a month.

Steege contended welfare recipients are attracted to Wisconsin for a variety of reasons, including its quality of life, lower crime rate, good schools, and to join family members who have previously moved there.

In November, 83,216 families in Wisconsin received AFDC, compared with 72,646 in 1980.