The RFC contains a mention that Monolog might be used, together with a question if it should be used directly or behind a facade. One should not bind to a specific logging library. If MW defines its own interface, which might be very similar to the one of the logging library, such binding can be avoided. One simple adepter would need to be created for each logging library that needs to be supported. This way other libraries can be used in the future, and changes to the library interfaces will not require changes to all of MW.
Topic on Talk:Requests for comment/Structured logging
If we go the route of using a third party library to implement the logging changes I would +1 using the PSR-3 Psr\Log\LoggerInterface as the expected API between MW and the logger implementation.