On the VMware Knowledge Base it reads:
When I start a virtual machine, I see a message box warning that says I do not have VMware Tools installed or I do not have the latest version of VMware Tools installed. I already have the latest version of VMware Tools installed or I don't wish to install the VMware Tools at this time. Can I turn off this warning message?
They suggest a neat per-machine solution based on editing a key in the virtual machine's configuration file.
Open your VM config file
If you know how to open a virtual machine's configuration file, skip to next step.
In VMWare Player select a virtual machine and hit Ctrl D. You get the virtual machine settings dialogue. Switch to the "Option" tab and you can read the virtual machine name and working directory.
Go to the working directory and you find
name.vmx, where name is the VM name: this is the configuration file.
VMware suggested solution
Add the following line anywhere in the configuration file:
tools.remindInstall = "FALSE"
Despite I set this key as suggested in the vmx config file, VMware Player keeps prompting to download VMware tools.