Will magnetic field of 12v DC micro motor mess up or destroy the memory of EEPROM chip if place it 2...3 cm away from the chip ?
Nope, the chip is silicon, non-magnetic.
I also think the eeprom will not be destroy but not for the reason indicated: magnetism is able to change the polarization of light in a fiber optic yet the glass is not magnetic. Magnetism is very complex.
However it may occurs interferences that affect the value of some bits and cause errors.
Only if you find any errors place a magnetic shield (soft iron) between the motor and the EEPROM
make a shield from cardboard , alu-foil and duct tape around the electronics.
That will not stop a magnetic field, so it is lucky that a magnetic field will not effect the EEPROM isn't it.
Even the strongest magnet you can get Your hands on, won't affect the EEprom, so you're safe.
BUT you can get electrical noise from the motor on the supply lines, and that can mess up the communication to the EEprom, so try to keep the supplies split.
// Per.