Check the front end parts, tie-rods, center link, ball joints etc. Also check the steering gearbox as well.
These didn't have very tight steering even when they were new but you should check the front end steering componets for wear, the steering gear has and adjustment on top that might help if that isn't worn out also.
Yes, called a worm gear adjustment screw, located close to the top front of your steering box, it has a slotted screw with a retaining nut , usually loosening the retaining but and turning this screw in a couple turns, will help reduce gear play, also a good idea to check the fluid level, generally 90 weight hypoid gear oil.
Unless equipped with power steering ! Do not put 90 weight oil in the steering gear box unless it is manual steering only.
Looking for a Used Impala in your area?
CarGurus has 35,425 nationwide Impala listings starting at $1,700.
Search Chevrolet Impala Questions
Are you a UK consumer? CarGurus now has a discussion forum in the UK.
Chevrolet Impala Experts