The message 'Wrong One - Moyes Out' will be carried by a plane hired by United fans to fly over Old Trafford during Saturday's match against Aston Villa.
The notion was put forward by members of online forum Red Issue, who are said to have raised £840 to carry out the fly-by protest.
The message relates to the 'Chosen One' banner at Old Trafford, which was unveiled in the Scotsman's honour after he took over from Sir Alex Ferguson last summer.
A number of United fans are growing increasingly frustrated with Moyes due to the club's current position of seventh in the Premier League table, 12 points adrift of a Champions League spot.
BBC journalist Dan Roan tweeted a picture of the banner, which is due to take to the skies tomorrow afternoon.
"Wrong One - Moyes Out"— Dan Roan (@danroan) March 28, 2014
My view of the banner for fly-by protest against ManU's David Moyes over Old Trafford tmrw pic.twitter.com/EmsKrG6zqO