Is possible to update the firmware of the PN532 chip?
I searched for "firmware" in the datasheet and this word pops up in only a few locations in the datasheet.

It mentions for example that the current consumption depends on the version of the firmware. That tells me that NXP determines what firmware is used on a particular chip.

Although a micro controller is used in this chip, I do not see how the end user can make use of that uC. As far as I can determine the uC is used to control reading/writing of data and generally controlling the IC. I do not see the possibility mentioned to load your own software into the uC.

Having that option to load your own software into the uC would require flash memory which would add cost to the manufacturing of these ICs. Since NXP sells these chips cheap and in huge quantities, my bet is that they use mask ROM and not flash ROM. 

Updating the contents of a mask ROM should require only one mask change so despite not being cheap the cost becomes much lower as more chips are sold with the new firmware version.

Using mask ROM will also save the cost of programming each chip before it leaves the factory as would be needed when using flash ROM.

So my answer is: No, you cannot update the firmware in this chip.