Speaking to the Times of Israel, Prince Turki al-Faisal said a deal could be considered only Israel acts as what he described as a "normal country".
He said: "Saudi Arabia is not considering a normalisation deal with Israel.
"Should Israel become a normal country with normal acceptance of international law, then Saudi Arabia will consider normalisation."
The TOI report noted that al-Faisal is "known for adopting a harsher tone against Israel than that of his government", but that "his positions have been reflective of Riyadh’s official stance".
And, asked about his country's insistence on Palestinian statehood, he added: "Realising the two-state solution requires a serious and trusted pathway that leads to the end goal, which is a viable Palestinian state as envisioned by the Arab Peace Initiative of 2002 and the vision of peace presented for a final settlement of this protracted conflict in that initiative.
"Normalising ties with Israel was conditioned by reaching that final and fair solution to the Palestinian cause."
But the prince suggested that previous peace processes have been "in vain" and that "Israel was not ready to pay the price of peace".