The FAA's standards require the use of GPS, i.e. the American satellites. This is covered in AC 20-138D, Airworthiness Approval of Positioning and Navigation Systems. It defines GPS:
k. Global Positioning System (GPS). GPS is a U.S. satellite-based radio navigation system that provides a global positioning service.
It also says that GLONASS and other non-US systems are not supported:
GLONASS is not yet approved for IFR operations in the U.S. National Airspace System
[...]
No FAA TSO exists for GLONASS, GPS/GLONASS, multi-constellation or dual-frequency avionics. Therefore, adding capability for any other constellation or dual-frequency capability must be accomplished as a non-TSO function until appropriate TSOs are available.
Apparently there is some kind of working group looking into using non-US GNSS but it's not possible yet. See Appendix 8 of the doc for full information.
