The State Services Commission is in the final stages of a recruitment process to find a permanent Director of the GCSB.
Ms Jagose has presided over the agency at a time of increased transparency and a push to improve public relations, after its activities came under intense scrutiny following a series of revelations and allegations.
A wide-ranging review of the SIS and GCSB, headed by former Deputy Prime Minister Sir Michael Cullen and lawyer Dame Patsy Reddy, is expected to report back by next month.