I want to know if there is any design criteria for the resistor placed between the gate of Power MOSFET (eg. IRF540) and the driving source (The driving source is an op amp and not a MOSFET driver IC).
A gate resistor is generally used to control switching time, so first you need to specify that. You also need to know the effective gate capacitance. You need a resistor that combines with the gate capacitance to give a RC time constant around what your desired switching time is. From there just experiment until you get it right.