Just trying to understand your question here-
So you have several ESXi hosts and you want to connect to them for monitoring purposes. You thought that vSphere rest API will help you achieve that but unfortunately vSphere is not present in your environment and now you want to know how you can install vSphere?
yes, Is this possible that VSphere is installed on hosts?
There is a ton of information available online about installing vCenter appliance on ESXi hosts (official documentation, blog posts, Youtube videos, etc.)
Here is a sample step-by-step tutorial covering installation of vCenter 6.7 server appliance: https://esxsi.com/2018/04/25/vcsa67/