The plane is due to fly over Old Trafford during their game with Aston Villa on Saturday.
Users on Twitter revealed the plan, asking for help raising funds:
They later claimed to have raised the money they required.
Daniel Taylor, writing in the Guardian, added that the message was also determined, and represented the most open challenge to the Moyes reign yet by fans:
Arrangements are being made for the plane to carry a message "Wrong One - Moyes Out" as a response to the "Chosen One" banner that has hung inside the stadium since the former Everton manager was appointed as Sir Alex Ferguson's successor.
If it goes ahead, the stunt will be the first concerted effort by fans to remove Moyes from his position in a season that has seen the runaway champions last year slump to seventh, 18 points off the top and guaranteed their worst-ever return in the Premier League era.
Other signs that attitudes are shifting include the Manchester Evening News producing a "Random Moyes Excuses Generator" on their site.