Contacting university for potential PhD collaboration without the presence of my supervisor
Actually it seems wiser to go ahead and look for suitable programs and doctoral advisors. It shows initiative that would be valued in most places. You don't need to accept anything, of course. But if people are interested (or not) it is good to know that. 

I find it hard to imagine a boss who would think it improper, though I've had some pretty bad ones. 

You never know what you'll find until you look. 

Moreover, once you are in a doctoral program your work supervisor will play little part. It is your doctoral supervisor who will be your guide.