Way 1 · best default
I'm saving up
You're putting money aside for something. Add "for" and the thing.
Examples
I can't come this weekend, I'm saving up for a car.
We're saving up to buy a flat next year.
In a conversation
A: Fancy a weekend in Paris next month?
B: I'd love to, but I'm saving up for my sister's wedding.
Common mistake
Not: I'm saving money for buy a car.
Say: I'm saving up for a car.
Use "for" + a noun (for a car) or "to" + a verb (to buy a car). Never "for buy".