Can I apply for a visa using both my new and old passports?

I am a Canadian living in Shanghai. When I go home to Canada this summer, I need to get a new Canadian passport, but the letter I am getting from my employer to get the F/ business visit visa has my old passport number on it. Can I apply for my visa using the new passport, if I present the letter and old passport at the time of application? I don't want my visa attached to a passport that is about to expire.