My mother tells the same stories everyday. I often say "mom you already told me that". Could this be an onset of Alzheimer's?

I do that too (but not everyday). I forget who I said what to. I talk to some friends frequently, others a couple of times a year.
So I tell my news (again) then the friends tell me “Oh yeah, you told me that.” Crud! 🥴
As far as I know, I don’t have dementia. I’ve got a better memory than my younger husband. 😉
I suppose I should write down who I say what to 😛 but it’s not that important to me.

Charlton Heston said when disclosed that he had ALZ that if he told the same story everyday to please just bear with him.

Maybe, and maybe not. Memory problems and repeating stories are also a "feature" of Mild Cognitive Impairment (MCI) which only progresses to dementia about 40% of the time. One relative displayed this problem when they developed geriatric diabetes and it went alway with treatment.

I recommend discussing this with the PCP to see what other health or medication issues could be causing/contributing.