You need to have an orientation defined for your object/entity. This is usually an unit vector in 3D, v=(vx,vy,vz). If you have an object oriented bounding box, then you can use that to determine where the "bottom" part of your object is. If not, just consider a "safety" distance/radius from the center of your object. Say this distance is d. Then one can simply find where the circle's center is by using the object's center, the v direction and the d distance:
CircleCenter = ObjectCenter - d * v
How to draw the circle? It might seem like a difficult task. In 2D, that's trivial:
circle(x,y,r) = (rcos(u) +x, rsin(u) + y), where u between [0, 360] degs.
In 3D you can draw it in the xOy plane, via its parametric equation:
circle(0,0,0,r) = (rcos(u), rsin(u), 0)
What to do next? Rotate the circle in such a way that its local Z(up) axis points in the same direction as the v vector. How? Find the rotation that aligns Z with v:
w = cross((0,0,1), v)
circle = RodriguesRotation(w, angle(v,(0,0,1)) * (r*cos(u), r*sin(u),0) + CircleCenter
The RodriguesRotation is the general rotation matrix against a w axis by an angle theta.
In the picture below, the black arrow is the orientation, the red circle with red orientation arrows is what your circle should look like, and the crimson line is the d distance offset from the object's center.