Dear Student,
We know that, according to ohm's law: V is proportional to R.
So, no current flows in an open circuit because the surrounding medium is highly insulating. So, theoretically, there is infinite resistance in the circuit. Hence, the potential difference can be considered to be nearly infinity
Whereas,there is a finite resistance offered by the circuit, in the case of an open circuit. So, we can say that in a closed circuit the potential difference between the terminals of the battery is infinite.
Regards