yes, Verizon will let you upgrade prior to your contract being up. Sometimes it is more than a month ahead. If you log into your Verizon account online, it should tell you if you are eligible for the upgrade.
if it doesnt say, just call them up or go to the store. You will have to sign another 2 year contract to get the special deal on the new phone.
If you are a good customer and pay all of your bills on time, I sure they wouldn't turn down the opportunity to make some more money off of you. Just call your local VZW office and they should be able to work with you. Verizon is the best!