I think that is not possible. The bootloader would have to include I2C code, and that would make it big.
The most used bootloader is OptiBoot : GitHub - Optiboot/optiboot: Small and Fast Bootloader for Arduino and other Atmel AVR chips
Here is a topic about it : Self burn by i2c EEPROM (bootloader) - Other Hardware Development - Arduino Forum
Tell us about your project. Perhaps there are other (and better) ways to achieve your goal.