The former Championship side can move back to being level on points with the Merseyside club if they manage to clinch victory over Manchester City on Saturday.
"All the pundits were talking about us finishing bottom of the league, so to finish above Liverpool would be unheard of, wouldn't it?" the Independent quotes Pilkington as saying.
"I'm from Blackburn-way up in the North West and that would be a great scalp. We've proved we're more than a match for anyone. We play Manchester City next and they need to beat us to stand any chance in the title race. But we'll carry on with what we're doing and try to take three points off them as well.
"We won't take our foot off the gas and we're hoping for another win against one of the best sides in Europe."
Norwich are currently 10th in the Premier League table.