It's also understood that Arsenal has agreed to loan the 18-year-old back to Saint-Etienne for the 2019-20 campaign in order for him to gain more experience.
Arsenal appeared to be close to completing a move for Saliba for €25 million (£22.5 million) earlier this month before Spurs reportedly swooped in with a €30-million (£27 million) bid.
However, it seems that Saliba has his heart set on a move to the Emirates Stadium.
Meanwhile, Ornstein adds that Arsenal will continue their pursuit of Celtic defender Kieran Tierney, even though the Scottish side rejected two offers for the 22-year-old. Arsenal's last bid was reportedly worth £25 million.