According to the documentation of Flask-SoskcetIO you can use async_mode to set async_mode. if you installed eventlet or gevent with gevent-websocket the websocket would be used first.
async_mode: The asynchronous model to use. See the Deployment
section in the documentation for a description of the
available options. Valid async modes are
``threading``, ``eventlet``, ``gevent`` and
``gevent_uwsgi``. If this argument is not given,
``eventlet`` is tried first, then ``gevent_uwsgi``,
then ``gevent``, and finally ``threading``. The
first async mode that has all its dependencies installed
is then one that is chosen.