Basque is the last pre-Indo-European language of western Europe and has no demonstrated relative. Proposals linking it to the Caucasian languages, to Iberian and to a wider Vasconic substrate have each been made and none has convinced. R. L. Trask, who assessed them, concluded that none of them meets the standard and that the honest answer is that we do not know, rather than that the relatives are contested. Aquitanian, the ancestor of Basque or its near relative, is attested only in Roman-era personal and divine names on inscriptions and reaches no further back.
What would resolve this New epigraphic material in Aquitanian or in a neighbouring undeciphered language, long enough to show grammar rather than names alone, would give the comparative method something to work with. A decipherment of Iberian that showed grammatical morphology rather than a shared writing system would settle the Iberian question either way. Failing new text, the answer is likely to stay open, because the comparative method cannot reach the required depth on the evidence that survives.
OpenHistorical linguistics, with palaeohispanic epigraphyR. L. Trask, The History of Basque