Compatibility between Asyncio and Eventlet has been recently introduced.
You may be interested by the state of the art of this compatibility and by the potential limitations, so please take a look at asyncio-compatibility.
Discover the Asyncio Hub <eventlet.hubs.asyncio>
You may also want to take a look to the Asyncio compatibility functions <eventlet.asyncio>.
Want to use Asyncio and Eventlet together or you simply want to migrate off of Eventlet?
Follow the official migration guide <migration-guide>.