is there any possibility to design an instrument transformer which has the characteristics of both current transformer as well as potential transformer? If yes, how can we proceed with such a proposition?
Theoretically you can say that a current transformer having say a single turn primary and multi-turn secondary to be turned around to function as a potential transformer by connecting the multi-turn winding between phase and ground, but practical limitations are that the CT must have either 1 or 5 amps full range rating and the PT must have 110 volt output.
If you wish to experiment it would be possible to get both characteristics in the laboratory but such a device would have no commercial utility.