Could I ask, what do you want a A320 rating on a Canadian license for? Anyone hiring for an A320 job in Canada would be providing the training for that aircraft, and already having the rating wouldn't enhance your chances of getting that job.
77AV8R has highlighted one of the main characteristics of aviation and Canada in general, the difficulty and expense in getting anything done even if you are willing to pay the cost. It's a heavily socialist country, if you don't fit in the system comrade, you're pretty much out of luck.
There are hoops to jump through to conduct training in the US for non-citizens, but they're hardly insurmountable. Any FSDO can walk you through that.
Do you hold any other license, ie FAA/EASA or other? If you really want a heavy jet rating on a Canadian license, other than working for a Canadian operator, it will probably be easier to do it somewhere else on another license and then transfer it to your Canadian one.
Otherwise Canada's industry and regulatory infrastructure is too small, insular, and protectionist to offer much assistance.