Suppose you are acting as Safety Pilot and PIC on a flight in IMC. Further suppose that the pilot at the controls is instrument rated but his or her IFR currency has expired. If the other pilot acts as sole manipulator of the controls during an approach, can you, as the PIC, log that approach as well? Assume the approach is loggable given weather conditions, etc.
No, a pilot may not log an approach that he or she did not perform as the sole manipulator of the controls.
According to the FAA, in order for a pilot to have performed a loggable approach, that pilot must have performed that approach as the sole manipulator of the controls. A required SIC may not log an approach that the PIC flew, nor may a PIC log an approach that was flown by the SIC. Likewise, a safety pilot, though he or she may be a required crewmember for a flight, may not log an approach that was performed by the other pilot.
This hinges on the FAA considering the word "performed" in 14 CFR 61.57 (c) to mean fly the approach as the sole manipulator of the controls. See the FAA's leter of interpretation Carpenter (1999) which addresses this issue:
As the SIC you have not "performed" the approach as contemplated by FAR 61.57(c) because you were not the sole manipulator of the controls during the approach.