Josephus seems to have believed in it, it is somewhere in “The war of the jews”.
I quote myself from a paper I once wrote:
This is a good connection to examine the extra-biblical usage of the word aionios at about the time the New Testament was written, before I turn to the Septuagint usage. The passages I will cite can be found at www.perseus.org. I will begin with the Jewish historian Flavius Josephus from the 1st century AD who witnessed the destruction of Jerusalem.
In “The Wars of the Jews”, Book 3, the English section begins at section 361, the underlined part is found section 374 in the Greek, he writes:
Do not you know that those who depart out of this life according to the law of nature, and pay
that debt which was received from God, when he that lent it us is pleased to require it back
again, enjoy eternal fame [kleos aiônion]; that their houses and their posterity are sure, that
their souls are pure and obedient, and obtain a most holy place in heaven, from whence, in the
revolutions of ages [peritropês aiônôn], they are again sent into pure bodies; while the souls
of those whose hands have acted madly against themselves are received by the darkest place
in Hades, and while God, who is their Father, punishes those that offend against either of
them in their posterity? for which reason God hates such doings, and the crime is punished by
our most wise legislator. Accordingly, our laws determine that the bodies of such as kill
themselves should be exposed till the sun be set, without burial, although at the same time it
be allowed by them to be lawful to bury our enemies (sooner).
Josephus seems to have believed in reincarnation, as surprisingly this might sound, he also described the Pharisees as to have believed in reincarnation, “eternal” fame is linked to their houses and their posterity, a place in heaven, from which however after eons they are sent back into pure bodies, so aionios in this context could rather be understood as something cyclical rather than endless, eonian fame until the next incarnation. A similar belief in reincarnation might be suggested in the Apocrypha, in Wisdom 8:19.20; John 9:2 might further confirm that the idea of reincarnation was not entirely foreign to the Jewish thought at the time of Christ, the idea seems to have derived from Platonism, but this is not the topic here.