This is a bad idea - explain to your client that it's against the principles of HTTP.
For example, a customer opens different pages of your site in two tabs/windows. The close the second one, and go back to the first tab, but not it's logged out and any link/page submit is going to cause an error. That would piss me right off.
Instead you should look at options like a short login timeout (e.g. 10-15 minutes if it's really sensitive data).