Only about 300 tickets have been sold for the away section at Tannadice after Rangers refused their allocation amid planned boycotts from supporters' groups.
Many fans have been unhappy with Thompson since United charged for a rearranged game after a match against Rangers was abandoned at Tannadice in 2009.
But much of the anger appears to stem from their perceptions of Thompson's attitude to dealing with the fallout of the financial collapse of the oldco Rangers in the summer, although United were one of 10 clubs to vote against the newco Rangers' application to join the Scottish Premier League.
Rangers manager Ally McCoist yesterday addressed fellow Scottish Football League clubs amid the Ibrox side's opposition to current plans to reform the Scottish leagues.
And Thompson hopes the fifth-round tie can be a watershed moment.
"Personally for the sake of Scottish football, I think we should move on," he told BBC Scotland.
"It's a game of football after all. That's what I'm looking forward to tomorrow.
"Hopefully it's a good and entertaining game. Hopefully my team will win of course. But we are in the middle of reconstruction talks and the game is moving forward.
"We have got all SPL clubs actually together to move forward for the future and I think we all need to get together, every single club in Scotland, and it would be good for them (Rangers) to come on board as well."