I'm aware that this post may not make sense to many people, but to one who wants to make use of their super-old hardware, this post is good news :)

To install we would be manually building docker on the host machine. To proceed clone this repo and run the following commands.

git clone https://github.com/docker-32bit/ubuntu
cd ubuntu
sudo ./build-image.sh

After a while the process completes and you can check whether docker is working by running the following command.

docker ps

Now to run docker without sudo we need to add your username to the docker group. To do this run the following command.

sudo usermod -aG docker $USER

Hopefully, your docker is working but after a system reboot docker engine doesn't automatically start. To enable the docker daemon to run on startup run the following commands.

sudo systemctl enable docker
sudo systemctl start docker

That's it. Now you have docker running on your 32-bit machine. To upgrade docker run the build command once again.

Thanks! If you have any issues please comment and I'll see if I can help.