It's not going to move for ten thousand years, and even if it did sooner, manmade excavation can keep it where it is now...
The Corps of Engineers has been "keeping it where it is" for several generations now. If not for their herculean efforts, it would have long since diverted itself to the course of the Atchafalya river, which already carries some of the flow of the Mississippi from just south of Natchez, near where the Red River flows into the Mississippi.
It almost jumped in 1973. It could happen 500 years from now or next year. But IMO it's best to be proactive, especially since we are faced with rebuilding anyway.