Load balance long-lived connections upon auto scale-out or scale-in of Envoy

Consider a scenario where there is auto scale-out of Envoy. In such a situation, I would actually like to drain few connections from an old instance and transfer that load to the newly scaled-out instance. Currently, I cannot find a way to drain a certain amount of connections an Envoy instance handles.

Would it be possible to have some sort of configuration where we could set the percentage of connections to drain based on certain parameters like number of connections per envoy instance or the total number of connections ?