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Make any elliptical selection. Then invoke Select-Transform Selection.

Now make 4 simple moves:

Move the left side of the Transform bounding box up to the leftmost point of the circle.

Move the right side of the Transform bounding box to the rightmost point of the circle.

Move the top side of the Transform bounding box to the topmost point of the circle.

And finally - move the bottom side of the Transform bounding box to the bottom point of the circle.

This way you won't have to manually center the selection around the circle by try and probe. Once you allign the Transform bounding box sides with the uttermost points of the circle the selection will be centered ans sized automatically.