The North West side have been second best in the two clubs' previous meetings, with the Spanish giants claiming the Champions League trophy over them twice in two years.
"[Catching Barcelona is] always going to be the challenge," The Mirror quotes Ferguson as saying. "We've introduced some young players to the club this season who have tremendous ability and a great energy and spirit about them.
"So I think we're making great strides towards that level Barcelona have reached these past two or three years."
United defender Nemanja Vidic was sent off in the Premier League champions' 2-0 victory over Otelul Galati in the Champions League last night.