Carrick performed well keeping Andy Carroll quiet on Saturday, but the pace of Alvaro Negredo, who is expected to lead the line for City in the absence of the injured Sergio Aguero, will present the England midfielder with a different and perhaps more dangerous threat.
Moyes said: "Michael did great at centre-half. He's played there before so it wasn't a problem.
"We even considered putting (Marouane) Fellaini back there as well, so I think we've got people who can do that if we have to.
"We gave Patrice Evra a rest but if we have to, I think we can put him there as well and he would cope manfully.
"It was great that the squad mucked in and that's the way it should be, when you are short in areas and it's all hands to the pumps.
"We were short on Saturday and Michael certainly played really well."
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