Accies head into their quarter-final clash with Irn-Bru First Division rivals Falkirk aiming to clinch a rare last-four berth and a possible showpiece afternoon at Hampden.
The Lanarkshire side have enjoyed some decent cup runs under Reid's guidance in recent years, but the New Douglas Park boss is eager to go one step better this time around.
He said: "I am reminded it was 1935 the last time we reached the semi-final of the tournament.
"This is my third quarter-final in seven years, so it is good to get an opportunity to get to the semis.
"In 2006, we drew 0-0 at home to Dundee and lost 3-2 in the replay after extra-time, which was a kick in the teeth.
"And then we were comprehensively beaten when we lost 5-1 to Rangers in 2009.
"This is a fantastic opportunity for us to get to the semi with it being a home tie.
"We have two had two away games against Dumbarton and Dunfermline, and this is a chance to create another bit of history at the club.
"It is a big thing financially for any club in Scotland, and not just Hamilton.
"Where we are at the moment, it would certainly be a big kick for us to get into the last four.
"It is achievable. We are playing a Falkirk side in a rich vein of form and they have won their last three games without conceding a goal. They will come here with plenty of confidence, but there is not a lot between the sides."
While Hamilton's Scottish Cup form has been impressive as they have seen off Dumbarton and Dunfermline to reach the last eight, their league form has been mixed.
Accies are just two points outside the Irn-Bru First Division relegation zone, but Reid knows the road back to the top will be a long one as they look to rebuild with another group of promising kids.
He said: "We had three years in the SPL, which is unsurpassed at this club. We lost key players so we had to build again and the First Division is not an easy league.
"I have been really buoyed by some of the football which has been played in this division. There are some really good football teams and we have found it difficult to be at the top end of the table.
"But we are building and we will get there again over the next couple of seasons."