I doubt ESXi will install fully on those Optiplex desktops (I'd be surprised if they supported hardware virtualization, and other components may not have drivers as well), and they would be unsupported in any case. Deploying ESXi to Optiplex desktops won't work.
If you need to use the local resources of the desktops and want to PXE boot the images to them. VMware doesn't have a product that offers that. Citrix Provisioning Server will allow you to do that for Windows OSes (Linux, etc. will not work), but is not a VMware product.
If you can create virtual machines on servers (e.g. Dell PowerEdge not Dell Optiplex) and deliver access to them to the desktops (using the servers resources, and the desktops are just a client to connect in) then VMware View will work following a traditional virtual desktop model. Linux is not supported here either.
Another option, which will use the local resources, is to install VMware Workstation in a locked down manner on these machines. Workstation will run on either Windows or Linux and can serve both Windows and Linux operating systems.