Understanding the Requirement: The application running on EC2 instances in private subnets needs to securely connect to an Amazon SQS queue without exposing traffic to the public internet.

Analysis of Options:

Interface VPC Endpoint in Private Subnets: Allows private, secure connectivity to SQS without using the public internet.Configuring security groups ensures controlled access from EC2 instances.

Interface VPC Endpoint in Public Subnets: Not necessary for private EC2 instances and exposes additional security risks.

Gateway Endpoint: Gateway endpoints are not supported for SQS; they are used for services like S3 and DynamoDB.

NAT Gateway with IAM Role: Increases costs and complexity compared to using an interface VPC endpoint directly.

Best Solution:

Interface VPC Endpoint in Private Subnets: This option ensures secure, private connectivity to SQS, meeting the requirement with minimal complexity and optimal security.