operational amplifier - Avoid leakage current

I use an opamp driver to pump several amps through an LED. My circuit is below.

^{simulate this circuit – Schematic created using CircuitLab}

When the input is low, I see a small leakage which I suspect is due to Offset Voltage of the opamp between the +/- terminals. 500uV is the Opamps' input offset voltage and the leakage current is 1mA.

I like to avoid this leakage but it is not easy to fix the offset voltage of the Opamp. How can I modify this circuit to avoid any leakage?

My input is a digital signal between 0 and 2.5V.