What's the best ways for a management server (from the public cloud) to access the REST APIs serving from a server sitting in the private networks?

We have a management server and UI sitting in the public cloud (Azure). We have a server which sits in our private networks, and it serves some REST APIs.

We want to access these REST APIs from the UI of the management (in the public cloud) to the REST API server serving from the private networks. The REST API server sitting in the private networks does not have a public IP address and hence the cloud UI/ management server cannot access it directly. What's the best way to handle this problem?

Would it be a good way to make the REST API server (which is sitting in the private networks) to initiate websocket connections to the cloud UI/ management, and then allowing the UI/ management (which becomes the client in this case) to initiate API requests within the websocket to the REST API server which sits in the private networks?