Well Liverpool is history at this point, so it's possible. United is another story.
They need to win the league every season for the next 10 years (and win 5 FA Cups) to match Arsenal's record. The Sheikh would die of old age before they got close to Liverpool or United's. Besides FFP is coming up soon, and either their oil will run out or the sheikh will get bored. It can't go on forever.
They've invested a shit-ton in a new academy.