The Scot has yet to taste victory at Old Trafford, while Ian Holloway is hoping for a repeat of the Eagles' shock League Cup triumph in 2011 as he serves a touchline ban
The defending Premier League champions head into the game against Ian Holloway's men after suffering a 1-0 defeat to fierce rivals Liverpool before the international break.
United are just one point ahead of Palace - who earned their first win of the season with a 3-1 triumph over Sunderland at Selhurst Park - after the first three games, with their only success coming on the opening day against Swansea.
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The defeat at Anfield - which followed a dour 0-0 home draw with Chelsea - marked the first time that United have failed to score in consecutive league matches since 2007.
However, Moyes, who never won at Old Trafford while in charge of Everton, should be confident of earning his first victory on home soil against a Palace team that has collected just 25 points from their last 24 league games on their travels.
United will be boosted by the presence of Marouane Fellaini, a deadline-day signing from Everton in midfield, but Wayne Rooney misses out with a head injury.
Phil Jones (ankle) and Rafael (hamstring) are also doubts, and Palace will travel north with some hope having beaten United in the League Cup in 2011.
If they are to repeat that feat on Saturday, then they will have to do it without Holloway on the sidelines after he was handed a two-game ban for comments made about referee Mark Clattenburg in the aftermath of their 1-0 defeat to Tottenham.
Although he will not be able to send out instructions directly from the touchline, the former Blackpool boss is excited at the prospect of facing United, and insists that his team will produce a positive showing.
"Let's enjoy it. I'm excited by all these games, but it's just another game," Holloway told reporters. "I believe the lads are getting together and believe they can get to grips with this division.
"I certainly won't be parking the bus. We have to go there and make a good account of ourselves.
"Palace beat Man United in the cup two years ago, I watched it on television. Can we go there and do it again?
"All I want is a performance. Let’s see what we can do."
Holloway has injury worries of his own, with Paddy McCarthy (groin), Yannick Bolasie (hamstring), Jerome Thomas (ankle) and Glenn Murray (knee) all still unavailable, while new signing Jack Hunt has a broken ankle.
Florian Marange, Stephen Dobbie and Owen Garvan have all been omitted from the 25-man squad.