nios ii and interfacing of ITG-3200 using i2cbus

It is of course possible to interface, but you will have to either find an I2C VHDL implementation or write it yourself. I assume you wish to initialize the chip, then read the gyro values, integrate them, and make then available via another communication channel to another device? Or perhaps rather than communicating the data, use it directly for some control system?

If you are able to write the VHDL for the integration, and communication/control, I would think you have the skills to write a simple I2C interface. Many people using micros that do not have an I2C peripheral will bit bang an I2C interface. You can do the bit bang approach on your FPGA.