The following code should do what you are asking. Attach this to your circle sprite.
extends Sprite
var pixel_remainder = Vector2(0, 0)
const RADIUS = 32 * 6
func _process(delta):
var mouse_pos = get_viewport().get_mouse_position()
var distance = mouse_pos.distance_to(self.position)
if distance < RADIUS:
pixel_remainder += (mouse_pos - self.position).normalized()
var push = Vector2(int(pixel_remainder.x), int(pixel_remainder.y))
pixel_remainder -= push
Input.warp_mouse_position(mouse_pos + push)
It looks like this:
