On my Trek Domane SLR the end of the front brake cable touches the tire. It makes an enerving sound and I am a afraid it destroys my tire. I thought about using some tape, but that is not possible because of the moving brake arm. Is there any possibility to push the cable to the side without renewing the while cable?
Chris H has the right idea. Eventually when you replace the brake cables leave it long so you can tuck it on the outside of the brake pad. For the time being i agree with Chris, do what you can to try and prevent it from rubbing because over time it will wear a groove in the tire if it hasn't already.
Here is an image from Trek`s website showing how they have it long and tucked to the side. Nice brakes but the cable routing leaves some to be desired in my opinion.
It looks like it's been cut too short so can't be tucked out of the way. But you may be able to cut it still shorter and use a smaller end cap/ferrule, or just part of one, or a blob of glue to stop the end fraying.
Bending the cable may work too -- you might not have enough length but a sharp bend away from the tyre might work. Use longnose pliers. This stopped my front derailleur cable irritating my leg, for example.
You're right to want to fix it -- metal rubbing on tyres isn't a good thing.
In addition to the the other options here, you may try extending the cable, or at least pretending like you're extending the cable - get some metal tube or maybe even a stiff plastic and crimp/glue it to the metal ferrule at the current end of the cable, then you may be able to extend that long enough to keep the end away from the tire.