A XDA user "EmersonTR" has managed to capture the Moto G4 Play Android 7.1.1 OTA update, meaning that owners of the Moto G4 Play codename HARPIA can install the update right now if they wish to (link to XDA post at the bottom of the page). But before you do, there are a few things to consider-
EmersonTR has stated that this update can only be flashed on Moto G4 Play ((XT160, XT1603, XT1604, and XT1607). Note that this OTA file is for the Moto G4 Play, so do not attempt to flash it on other devices.
We recommend you to wait for the official OTA, as Motorola is about to push the update. The company earlier confirmed that they will update the Moto G4 Play to Android Nougat by June, 2017, but it seems that the company is still testing the firmware with the MFN users.