No, never ever store contacts in water. Even if it is purified, water from a tap can contain bacteria or microorganisms that can lead to severe eye infections.
Plus, water will not disinfect contact lenses. If you put them in water in just a few minutes or a few hours, bacteria, pathogens, and fungi can grow on your lenses and get into your eyes.
This is why eye professionals tell their patients or customers to take out their contact lenses whenever swimming no matter if it is in the ocean, a lake or in a pool. The microorganisms that live in water can remain on the lenses and cause eye problems.
You should wear swim goggles, at the very least, when swimming if you do not take out your contacts. These will protect the lenses and your eyes. If you wear disposables, you can also swim with them and then discard them afterward, replacing them with a new pair.
You can read more about good strategies for swimming when wearing contact lenses here.
Putting Contacts in Water is Risky and Uncomfortable
This is the harsh truth. Eye infections from dirty or improperly disinfected contact lenses can cause vision loss and permanent eye problems or blindness.
Only use approved contact lens cleaning solution. Water - even distilled water - does not have the salt that your tears have, and it is not balanced to handle your tears' acidity.
Due to these differences, water can make your contact lenses become misshapen and stick to your eyes if you try putting them on. It can cause obvious changes in vision or blurriness.