Seems very easy :)
Grid disable / Straight Snap enable / Object Snap Enable
Draw a circle (so center is marked as "hot snap" point!)
call Rectangle by center
draw an helper line horizontal tangent by the "Quadran hot snap" of the circle
Now Box rectangular by center can be drawn!
Click center Circle, Click Intersection ("Square", "Intersection" helper line)

= You have your box (a square) around the circle, and can manipulate now with it own box "edit frame"
Can't be more simple ;) (an half second realized)