According to the Football Leaks website, which has uncovered details of other player contracts in the past, the Reds added an £82m release clause allowing him to talk to another club that met the valuation, with the exception of Arsenal.
This unusual stipulation appears to be related to a problem between the two clubs over Luis Suarez
In 2013 Arsenal tried to trigger a release clause by offering £40,000,000.01, but Liverpool had carefully worded the contract to allow them to have the final say.
It now looks like the fallout from those events now appear to have dictated the terms in Firmino's contract in order to prevent a recurrence.
Source: DSG