Hull have drawn Southend United in the Fourth Round.
Harper is honest enough to admit the FA Cup must play second fiddle to Premier League survival this season, but his romantic side is still daring to dream in what could yet be his final tilt at glory.
He told the Hull Daily Mail: "It would be great to win silverware but the priority for a newly-promoted team is to try and stay in the Premier League," said Harper, who is currently undecided what will come next at the end of his contract.
"When these games come along it gives those of us who haven't had as much action as the other lads to get up to speed. Hopefully, that means a positive result and we stay in the draw. Who knows where it can take you?
"It's still a very prestigious tournament but the Premier League has grown to be this mammoth competition, arguably the biggest league in the world, and that's taken the edge off what is the oldest and most prestigious competition in the world."
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