Having a chip capable of FM reception is not enough - there has to be a suitable FM band antenna and the current iPhones lack this. Because of the frequencies of the FM band, the antenna has to be MUCH larger than the internal cell network, WiFI and Bluetooth antennas to get adequate signal.
The Nano and other phones that have FM use the wires of the headset as an external FM antenna. There's no indication that the current iPhones are wired to do this. It would also preclude having FM with Bluetooth headsets or using the internal speaker.