Access API running on-prem from private EKS cluster pods

Question

IHAC having EKS cluster running on private subnets and needs to access API running on-prem. CX has DX connection to on-prem that is connected via CGW. Access through EC2 is allowed but pods can't access the on-prem url. We enabled SNAT on pods but it says NAT gateway is required to do so. What is the correct pattern for above access using DX for EKS pods?

Answer

What about using Route 53 Resolver Outbound Endpoint?  
This can be used to resolve on-premises DNS names.  
https://docs.aws.amazon.com/Route53/latest/DeveloperGuide/resolver-forwarding-outbound-queries.html

Or you could set up a private host zone in the VPC, etc.  
https://docs.aws.amazon.com/Route53/latest/DeveloperGuide/hosted-zones-private.html

Access API running on-prem from private EKS cluster pods

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