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
A current is created due to the potential difference in a circuit (which means when one side of the circuit has more + charges than the other side (and vice-versa for the other side))), this causes a charge to flow from one side
to the other(current). When its open due you think it will ever reach the other side? And even consider that potential drop only exists in the circuit (meaning the battery and wires). If they are not connected (closed), how will a potential drop exist?

And therefore consider, if there will be a flow of charge without a potential drop?

To your statement: *"I = 0 in open circuit because of potential difference"* - I do not think thats true.

Consider the simple Ohms law, that relates potential drop and current: $$V=IR$$where $R > 0$ (otherwise you have a short circuit). If $V = 0$, then $I = 0$, as $R > 0$. If there is a potential drop without a current, then either the resistance is $\infty$, or the system is malfunctioning or simply your circuit is non-ohmic.

*"Now, a chemical reaction happens in the cell which makes the current to flow in the wire"* - "**chemical reaction**" - this is not what causes current to flow in the circuit. Remember its the potential drop (imbalance of charges on either ends of the closed circuit (or cell)). You cannot force the flow of charge (electrons) just because of a chemical reaction...