Arsenal will be the perfect game for him, IMO. Özil is a master manipulator of space who keeps popping up in dangerous positions, but not that fast in short bursts as far as lateral movement is concerned, and Carrick can be used as the cerebral holder to screen him. Not mark him per se, but try to limit his influence by controlling the flow of the ball, thereby limiting his interaction with Sánchez - that coupling is probably their biggest offensive threat. Pogba and Ander ahead of him will provide the exuberance to match their central midfield pairing, and their quicker guys on the outside will seek to exploit our fullback/central defender zone, for the most part.
Schneiderlin is more athletic, but I don't trust him to: a) open up our offense and control the game in the way it needs to be controlled, or b) act as the experienced holder in front of the defense (which will be a weak spot by the look of things - necessitating a seasoned touch in terms of spatial awareness). Plus, managing the tempo of the game could be vital against Arsenal, and Carrick could help mount a 'controlled onslaught' from midfield. Who knows, though, we could even start with Fellaini in the Anfield setup. Wouldn't be a proactive choice, but as long as it helps us put more points on the board.
Ooh, also - Arsenal might start off quick from the get go, or atleast that's what I'd want my team to do against United. And without Carrick, going 1-2 goals down early on could trigger a meltdown that we likely won't recover from. His composure in tricky situations is not to be undermined.