After memorable victories over Millwall, Chelsea and Sunderland earlier in the competition, Championship side Reading stand in the Bantams' way of a place in the last four of the competition and a trip to Wembley Stadium.
City's only previous visit to the semi finals of the F.A Cup came way back in 1911 - the year of the Bantams' one win in the competition so far.
Given the importance of Saturday's eagerly-anticipated tie then, Davies knows Phil Parkinson's side must do all they can to keep the club's dream run in the F.A Cup going for at least one more match.
Davies: "This has been a great run for the club in this competition.
"Who could have pictured us winning at Chelsea and then beating Sunderland?
"It has been an unbelievable run for us so far and one that most people probably wouldn't have predicted if we're being honest.
"It is full credit to the manager and the staff like (assistant manager) Steve Parkin, who perhaps doesn't get the credit he deserves sometimes.
"It is big credit to everyone at the club as well for helping us to get this far.
"We will be doing everything in our power to keep this run going and going. We have to try and carry this on as long as possible because you never know if or when we'll get the chance to get this far again.
"You don't get to the quarter finals of the F.A Cup every week in your career so it is a massive occasion for all of us.
"We know the prize that is waiting the winner's of Saturday's match and we really want to grab it if we can.
"We will be doing everything in our power to help the club into the semis.
"I've watched Middlesbrough in F.A Cup semi finals as a kid and I never thought I'd get the opportunity to get anywhere near one as a player.
"We are within touching distance of it now and we really want to take advantage of this opportunity we have."
Following on from City's victory over Sunderland in front of a packed Coral Windows Stadium in the previous round, another full house is expected for the visit of Reading this weekend.
Davies added: "We play at a fantastic stadium and to see it full against Sunderland was an amazing experience.
"The support really drove us forward that day.
"We are buzzing to have that experience again."