Try a correct sized wooden lathe that has been pre-treated then set it on a bed of window frame silicone sealant then point the outside edges with the same sealant, making sure all gaps are sealed where it butts up to the garage.
You will probably also have to drill through and screw it down to the base a few times, to make sure the weight of your car does not move the timber.
Failing that you could to cut out a gulley across the font of the doors and put in some drainage channel blocks that you can buy from builders merchants, but that will be more difficult and expensive.