The Premier League champions stand in the way of the Magpies and a spot in the quarter-finals, but Janmaat is refusing to give up on the hope of lifting silverware this season following Sunday's morale-boosting victory over Tottenham Hotspur.
"Of course, it is a prize and Newcastle have not won one since 1969," the Dutch defender is quoted as saying by The Mirror. "It would be a great party if we won a prize. The fans want that very much.
"City have a big squad and a great squad - even their second team is very good. It will be a tough game, but if we play like we did in the second half at Spurs, then of course we have a chance."
Newcastle reached round four thanks to a dramatic 3-2 victory over Crystal Palace last month.