Cherries are known for having large surface roots which run horizontally and which often produce sucker growth as the plant matures. You've not said which variety of tree you have, so making a judgement about how far the roots might run is difficult - they vary in size from dwarf weeping at about 12 feet high up to 45 feet or more in height, and the size of the tree is equivalent to the root spread. As a general rule, trees should not be planted less than 40 feet away from a house or structure with foundations.

I would consult an abourculturist and get his advise. My fathers cherry tree cause considerable damage to the drain system blocking them up causing rising damp and cracked driveway.

Very expensive for repairs and then to have the tree removed professionally.

If it's a big tree I certainly wouldn't advise cutting it down yourself.