JÑĀNĪ AND REBIRTH
It is said that a man of knowledge, jñānī, has no rebirth. How so? Because jñānī knows that there is no birth in the first place! The question of re-birth arises only if one accepts the fact of birth. The jñānī knows that in Me, the Eternal Consciousness, countless births appear, but, I, the Eternal Consciousness, is not subject to births and deaths.
The Bhagavad Gītā 2.20 puts it most succinctly:
न जायते म्रियते वा कदाचिन्
नायं भूत्वा भविता वा न भूयः
अजो नित्यः शाश्वतोयं पुराणो
न हन्यते हन्यमाने शरीरे २.२०
na jāyate mriyate vā kadācin
nāyaṃ bhūtvā bhavitā vā na bhūyaḥ
ajo nityaḥ śāśvatoyaṃ purāṇo
na hanyate hanyamāne śarīre 2.20
The Self is never born nor dies;
nor does it come into being only after being born.
It is unborn, eternal, everlasting, and primeval;
It is not killed when the body is killed.
The illumined person knows the eternality of his or her real Self.
He crosses the sea of sorrow with the raft of this knowledge.
S/he is not subject to the cyclic rounds of births and deaths.
 Based on Swami Paramarthananda ji’s Discourses on Śrī Dakśiṇāmūrti Stotram, discourse # 10 of 16.