The London derby has been identified as a high-risk match due to the rivalry between the supporters and Harris has appealed to both sets of fans to maintain order and enjoy the game at White Hart Lane.
He said: "It will be a terrific atmosphere that's for sure.
"Our fans are going to travel in numbers and I want them to enjoy themselves and enjoy an FA Cup quarter-final occasion. Support the team.
"I'd say to both sets of fans just come and enjoy the game and certainly be proud of your team but be loud also.
"It can certainly bring some good press for us. As a club, of course you want to paint yourself in the right light. It is a competition that has been good to us this year. We certainly want the focus to be on on-pitch activities.
"We could have sold out our allocation three or four times over because they're proud of the players they see at the moment.
"Tottenham have a great following. White Hart Lane is a football cathedral with a good passionate crowd. It's the last game at the Lane in the FA Cup.
"Millwall in town with nearly 4,000 fans is going to be an electric atmosphere, one we should all embrace and look forward to."