Unfortunately having only a projected rectangle does not define how a circle should be projected. A projected rectangle can present infinitely different rectangles seen in different projections. To remove the ambiguity you must have a square seen in the wanted projection.
Let's assume you have a properly projected square. It can be made using a descriptive geometry construction, calculated, copied from already existing image or simply drawn using artistic intuition "This is how a square is seen from my wiewpoint, no matter if it's a little tilted"
Fitting a circle to the square:

- draw a circle, select it
- insert path effect Perspective Envelope
- select the envelope
- use the node tool, drag the corners to the corners of the projected square
Be sure you have enough snaps to points ON (crossings, nodes)