Disclosed herein is a method and a function entity for selecting a core network slice (NS), for serving a wireless communication device (WCD) 530 in a core network 500 comprising at least one a Management Function (MF) entity 530 serving the WCD 530 and at least one Repository Function (RF) entity (NRF1, NRF2) serving a plurality of core NSs (NSI #1, NSI #2) each comprising a plurality of Network Function (NF) entities the method being performed by a Slice Selection Function (SSF) entity 510 operative in the core network 500, the method comprising: obtaining 612, 616 NSI running status information indicating NSI miming status for each NS to be monitored; receiving 622 a NSI selection request comprising NSI selection information indicating at least one of NS (NSI #1, NSI #2) for serving the WCD and selecting 624, based on the NSI selection information and the NSI running status information, a selected NS (NSI #2) for serving the WCD.