It depends on the industry sector.
In financial services, regulators prefer separation of duties between program execution and program oversight. Program execution is most often attached to the procurement function. Alternatively, in smaller FI's it is part of IT or Finance. Oversight (policy ownership, receivers of risk reporting, etc) are universally in a risk function, Ops Risk if there is one.
Outside of financial services, it may be part of procurement, IT, legal or finance. There are no clear cut rules in the absence of regulatory oversight.
Hope this is helpful.
------------------------------
Linda Tuck Chapman, C3PRMP
CEO, Third Party Risk Institute
thirdpartyriskinstitute.com
------------------------------