Maybe the idea of such existing was mixed up with the occation where a monk told the Buddha that he would leave the holly life if he would not tell him whether there is a "Self" or not. In such way confronted the monk got hardly rebuked an asked if the Buddha ever told that he teaches, will teach such. (Link, later?) Going then back to his usual way of teaching dispassion.
But of course, to speculate about futher existences, likewise past or present, lies in the sphere of "I-making" (papanca, or craving-verbalisations). Of which my person guesses that the thought such "Enough" statment like in the OP-Question derives from.
"This is how he attends inappropriately: 'Was I in the past? Was I not in the past? What was I in the past? How was I in the past? Having been what, what was I in the past? Shall I be in the future? Shall I not be in the future? What shall I be in the future? How shall I be in the future? Having been what, what shall I be in the future?' Or else he is inwardly perplexed about the immediate present: 'Am I? Am I not? What am I? How am I? Where has this being come from? Where is it bound?' (MN 2]
there are 108 craving-verbalizations.
"This, monks is craving the ensnarer that has flowed along, spread out, and caught hold, with which this world is smothered & enveloped like a tangled skein, a knotted ball of string, like matted rushes and reeds, and does not go beyond transmigration, beyond the planes of deprivation, woe, & bad destinations." (AN 4.199)
The fact that "selves" get reborn is at least no encouragement to seek for it, and as also mentioned in the question: the Buddhas teachings are about getting dispassionate with1 all kinds of becoming. It (notion of self and it's possible harm or support) just used as a governing prinziple to gain a good notion of self. When ever there is no more notion of any self indentification then such as rebirth has come to an and.
Of course it is nonsense to speculate about "what" kind of rebirth if still subject, if there is still a condition for it. Of what rebirth one may gain next, the Buddha described with the falling of a stick thrown into the air, one time falling on this end, then this, or on the side (link later) But in regard that certain actions give certain results on ones being, when ever such may ripe, and there is rebirth if the is the condition for it, in this regard the Buddha was clear and did not let any door for speculation but encouraged one with it to better take the secure way and let short timely "fortune" and "misfortune" better behind: in putting an end to birth.
[Note: This is a gift of Dhamma and not meant for commercial purpose or other low wordily gains by means of trade and exchange.]