How nice is the lake there in Leazes Park?
I think getting it to be part of the bigger design, use it as an element, and build the new stadium just to the west of it, would be impactful. A beautiful new state of the arm stadium, right there, still on the hill. Still able to be seen from all around the city.
Something like SoFi Stadium in LA comes to mind with the lake element, but make it even cooler looking:
(article on fitting this stadium into the ecosystem: https://www.hksinc.com/our-news/articles/design-for-ecosystems-at-sofi-stadium/)
I just don't see the Saudi's not trying to build the best stadium in English football (if not world football) as close as possible to the current location. They will want to flex that financial power eventually. But I don't think they're out-of-touch enough to move it away from the city center.