Docker in kubernetes pod

We have a requirement where the host VM is not having docker installed.
But a custom Kubernetes pod needs the docker.sock file in which the docker images are pulled and keep on running inside the custom pod.
For docker daemon we need to run it as a separate pod and make it communicate with the above-mentioned custom pod.

If you don’t have Docker on the host, you don’t have a socket. So what is your goal? I understand that a pod needs the socket but why do you need the pod? If you want to build image sin Kubernetes, you can try something like GitHub - GoogleContainerTools/kaniko: Build Container Images In Kubernetes.