The Red Devils have not beaten Liverpool on their home turf in four years.
"We're long overdue a good result at Anfield," Cole told United's official website. "I thought we played well there earlier this season and Liverpool aren't scoring too many goals at the moment. I think we can go there with a real sense of belief."
Sir Alex Ferguson's side emerged as 1-0 winners when the two side faced each other in the cup last season.