Gov. George C. Wallace may give up his bid for a U.S. Senate seat if the state legislature doesn't vote Monday to provide permanent bodyguards for him, his aides say.

"He cannot go to Washington without the troopers," explained one assistant. State troopers have been in constant attendance upon the governor since the early 1960s. Since he was paralyzed in an assassination attempt in 1972, the troopers have provided mobility as well as security.

Bills to provide lifelong state aides for Wallace have been defeated in several recent legislative sessions. This session, which ends Monday, already has killed a bill that would have provided two state troopers at state expense for the rest of his life. When it was amended to prevent state funds being used for out-of-state trips, Wallace supporters killed it.

he bill now pending has been passed by the state House and would pay all expenses of two troopers anywhere, including permanent residence in Washington. It has not come before the state Senate. The order of introduction there is controlled tightly by the lieutenant governor, who has sought concessions or other issues from the governor's office.

The lieutenant governor, Jere Beasley, however, announced this week he favors providing the bodyguards. Beasley is a candidate to succeed Wallace as governor. (Wallace cannot succeed himself.)

An additional incentive to Wallace to drop out of the race for the seat being vacated by Sen. John J. Sparkman was offered in the form of a professor's chair at the University of Alabama's Birmingham campus.

Faculty discussions at the university have centered on the governor's joining the history department as a special professor specializing in recent state history.

Such a position would provide a salary of 5 percent of the proposed endowment, or about $25,000 a year, a university source said. A movement reportedly is under way to raise $500,000 to endow the seat.

As a professor, Wallace would be eligible for free professional care.

Wallace has denied through aides that he has received a firm offer from the university, but a Birmingham businessman says he received no discouragement from Wallace when he told him of the plan. The businessman, John M. Harbett III, is a contributor to Wallace's chief rival for the Senate seat.

Another option would be a position at the rehabilitation center where his physical therapist works, Wallace aides say.

Still another factor could influence the governor's decision: his standing in political polls here. Wallace's hardcore following is just under 40 percent, and recent polls show his support stable while that of his chief rival, former chief justice Howell Heflin, has begun a steady climb.

But aides say the bodyguard bill is his major concern. Explained one, all you've got to do is look at him to see why he needs them."