Question: [![enter image description here](https://i.stack.imgur.com/r18K6.jpg)](https://i.stack.imgur.com/r18K6.jpg)

This is an open circuit. Now, a chemical reaction happens in the cell which makes the current to flow in the wire. Then, the current has no other place to go, so it just gets grounded. It is similar to if I was holding the end of this circuit & put it on my finger. I would experience the current. So, the current does flow right. I do agree the circuit will not complete.

Why is it said that $I = 0$ in open circuit because of potential difference.

The charge inside the cell will move from the negative terminal to the end of circuit through chemical reaction inside the cell.

Answer: 
In simple terms initially there is a potential difference across the wires, current flows, due to the high resistance of air, charges will accummalate on the end of the wires, this charge accumulation creates a potential difference to counteract the batteries potential, once they are equal, no current flows
There is indeed [a very brief moment](https://physics.stackexchange.com/questions/531183/does-an-electric-current-flow-in-an-open-circuit) when the wires are attached to the terminals when a current flows, during which the wires are brought to the potential of the terminal.

There is no current otherwise, because as you mention the circuit is not closed.