Android 7.1, the latest Nougat-flavored iteration of the popular mobile operating system, brings a lot of benefits to the table. Among others, it manages battery, RAM, and processor usage better, implements new libraries which lets apps do new things with the system, and adds in support for movable, resizable windows. Chrome OS currently features an underlying Android framework that helps certain apps and system functions to run, and allows certain compatible Chromebooks to access the Play Store and a good chunk of the vast selection of Android apps available within its bounds. It's not hard to imagine how Chromebooks could benefit from the new features found in Android 7.1, which would mean that a version bump for that framework would have to happen. Currently, that framework is based on Android 6.0 (Marshmallow) in most Chromebooks, but a few recent finds in the Chrome OS codebase point towards the possibility of Android 7.1 becoming the new Android underbelly for Chrome OS in the very near future.
For starters, a piece of code in the open source Chromium repository that's primarily made for graphics library processing comes with a note. That note states that current Chrome OS devices have full support for Android 6.0, but that the Chromium team will need to be able to switch things over smoothly and easily when 7.1 becomes ready to implement in the internal framework. As if that weren't enough, the class-defining subfile attached to another commit makes reference to Android 7.1 as though it were made to be able to run on the newest version of Android. While this is no guarantee that we will see Android 7.1 in Chromebooks any time soon, it is a guarantee that the Chromium team is putting some serious thought and effort into the idea.
Currently, Play Store support on Chromebooks that have it available is in beta and rumors peg the feature as coming out of beta for most Chromebooks when Chrome OS version 55 drops, which will happen soon, providing there are no hangups or hitches. It's possible that the framework upgrade could come at that point, though this is merely speculation; right now, there is no hard evidence of any kind of time-frame for Android 7.1 to hit Chrome OS, only evidence that the groundwork is being laid for such an event to take place.