How to deploy API Gateway with template_file stored in s3 bucket?

Is it possible to setup template_file with yaml file stored on s3 bucket? Is there any other solution to attatch external file to API Gateway (like in case of lambda function which can be build based on file stored on s3)?

Update: I tried to combine api_gateway resource with s3_bucket_object as datasource but terraform probably do not see it. There is an information that there are no changes.

data "aws_s3_bucket_object" "open_api" {
  bucket = aws_s3_bucket.lambda_functions_bucket.bucket
  key    = "openapi-${var.current_api_version}.yaml"
}

resource "aws_api_gateway_rest_api" "default" {
  name    = "main-gateway"
  body    = data.aws_s3_bucket_object.open_api.body
  endpoint_configuration {
    types = ["REGIONAL"]
  }
}

I tried also achieve it by using template_file

data "aws_s3_bucket_object" "open_api" {
  bucket = aws_s3_bucket.lambda_functions_bucket.bucket
  key    = "openapi-${var.current_api_version}.yaml"
}

data "template_file" "open_api" {
  template = data.aws_s3_bucket_object.open_api.body
  vars     = {
    lambda_invocation_arn_user_post    = aws_lambda_function.user_post.invoke_arn
    lambda_invocation_arn_webhook_post = aws_lambda_function.webhook_post.invoke_arn
  }
}

resource "aws_api_gateway_rest_api" "default" {
  name    = "main-gateway"
  body    = data.template_file.open_api.rendered
  endpoint_configuration {
    types = ["REGIONAL"]
  }
}

but result is the same.