Roots are not the issue. Cordylines are root hardy and send up pups. If you do not want a multistem plant then cut out the ones that you do not want.

I was wondering if the Cordyline would do any damage so close to the house.(:0)

The roots should be fairly easy to trim if need be, but just how close is it to the wall? Are you restricting the top growth? If it's not too big, it might be worth considering moving it to somewhere that will give it space to grow.

Roots won't be a problem at all, there's hardly anything to them.

I remember how many questions we had about 'dead' Cordylines. I have seen many with numerous new sprouts that have re-grown. So our advice to see what happens was right after all!

Thanks all......I believe it's a combination of wet and freezing temps that cause them to rot in the middle, I lost two lovely ones that year. I also thought I had lost a nice Phormium tried to get root out but couldn't do it so left it and it sprouted again and looked better...the Gardeners Mantra, wait and see (:0)

The roots of a Cordyline do not affect buildings.

Yes, the roots of Cordylines, like yuccas and true palms are fibrous and do not expand. The base of the trunk(s) will expand, however, and may wind up pushing against the foundations.