I think it depends on your climate re: basil plant going from outside to inside. I had some luck keeping a tiny leafed basil plant from outside going in but not so much the typical larger leafed. I have had luck cutting stems from an outside plant and then just putting it in water in like a vase or mason jar - that will usually last a month+ and keeps growing (and even roots)!
LIke @4kids4us I recommend giving something a try but if fails, grab a plant from TJ’s or your grocery store produce department - they are more suited for indoors and sort of go indoors to indoors instead of outside to indoors.