The only time Sterling has been mentioned is “if Chelsea sell him”. There has not been a link to an actual interested club. Saudis have been mentioned, but just in general possible destination. No Saudi club has been rumored to make an approach.
I would wait until this all plays out. There are several keepers linked to us. A negotiating tactic is often to show the selling club you really don’t need the player being discussed. The sporting directors can easily be trying to manipulate getting a keeper without paying the big club tax.