If your dept is planning in the future to make cuts at your position related to outsourcing than you can offer to volunteer. Please keep in mind I would speak to HR because your manager may be less than forthright about future planned layoffs at your position because they do not want to lose you. Fortunately my boss is a class act and helped facilitate it for my co-worker. My co-worker wanted to leave anyways and my boss does not end up having to let someone else go so everyone wins and no bad feelings.
I do not know how your manager operates but mine is the best and tells us everything. We always know well in advance what upper mgmt has planned for our dept in relation to how many bodies and when. State Street is mostly a garbage company now, but I am fortunate to work in one of the few diamonds in the rough.