I have a eucalptus tree in my small town garden. I'm very fond of this tree, have topped it but a little more concerned as to whether the root system could cause damage to my foundations.
Root System of Eucalyptus Tree
Certified GKH Gardening Expert
Eucalyptus roots tend to be shallow compared to other trees, going down about 6-10 feet normally. Therefore, it shouldn't pose much of a threat to your foundation; however, since this type of tree can be quite water hungry, its roots will tend to wander in search of water when not enough moisture is provided (most foundation planting areas are typically drier), which can ultimately lead to issues later unless you can maintain adequate moisture.