Cole, 33, revealed on Monday night that he is likely to leave Chelsea this summer after spending the past eight years at Stamford Bridge.
McGrath believes that the veteran full-back would be a good acquisition for the Red Devils amid reports that Patrice Evra could be on his way out of Old Trafford.
"I would have Ashley Cole every day of the week because since he has come back [into the Chelsea team] he has been a revelation," McGrath told talkSPORT. "He has been a brilliant player for Chelsea.
"That would be a good move, if you could somehow guarantee that he would be able to play the games."
Cole recently announced his international retirement after being left out of England's squad for the World Cup.