There is no ETA or plans I am aware of to support .NET Core in Cloud Services. Cloud Services is one of our classic products and new features are no longer being added. That being said, .NET core is something that is supported in Azure Web Apps or Service
fabric for example. So you might consider going that route instead.
There has been no public discussions around what will be replacing cloud services in the future. Once that announcement/ decision has been made they will be sure to share supported languages and what not.