From UEFA's constitution.
Article 5
1
Membership of UEFA is open to national football associations situated in the continent of Europe, based in a country which is recognised as an independent state by the majority of members of the United Nations, and which are responsible for the organisation and implementation of football-related matters in the territory of their country.
2
In exceptional circumstances, a national football association that is situated in another continent may be admitted to member- ship, provided that it is not a member of the Confederation of that continent, or of any other Confederation, and that FIFA approves its membership of UEFA.
So for Saudi clubs to enter the "UEFA Champions League", Saudi Arabia has to join UEFA. And that can only happen if FIFA approves (which they won't, because it kills the World Club Cup and they'd probably say no just to piss UEFA off anyway).
And then if they do enter the CL, as
@Richey points out, there's FFP considerations. Either the Saudi clubs have to meet FFP (which they won't) or UEFA has to absolve the other teams in the competition from following it (which they won't).
This is not going to happen.
And please don't tell me the Saudis will just go and "buy" UEFA and FIFA, that's just daft.