A memristor is a two terminal device that features a change in resistance depending on current flow history.
If op-amp(s) were used to emulate a memristor then they would require external power supplies. The memory element would probably be a charged capacitor, with a transconductance amplifier or FET as the variable resistive element.
You need to first define the characteristic curves that your memristor will follow. Then an emulation circuit can be designed to meet those requirements.