Many companies run after the promises of low cost with the same of higher quality expectations. Yet they have never even organized the service they want to outsource as a separate service within the company.
A good first step to check the feasibility, is to work out the how you would organize the separate service in your own company... this should bring some clarity about which parts you want to keep inside the company, service level agreements, constraints such as language barriers and time-shifts, versus the goals of the business.
Once you have defined the 'service' within your business, it should be much easier to outsource that specific function.
Hope this helps.