From the FCOM (737NG)
Raw Data Monitoring
During localizer-based approaches (ILS G/S out, LOC) applicable raw data must be monitored throughout the approach.
During non-localizer based approaches where the FMC is used for course or path tracking (VOR, TACAN, NDB, RNAV, GPS, etc.), monitoring raw data is recommended, if available.
During single FMC, single IRU, or single DME or single GPS operation, in the event the single operational FMC, IRU, DME, or GPS fails during the FMC approach, there must be a non-FMC means of navigation available for a missed approach such as VOR/NDB raw data and/or radar, and there must be a non – FMC approach available. Failure of the remaining single DME need not be considered if GPS updating is being used.
Which means under normal operation (2 FMC 2 GPS) there is no need to monitor the navaid on which the approach is based (except for LOC/ILS/GLS). It is of course recommended, but not required.