The Hoops were the first name out of the hat and were handed a third-round meeting with Raith Rovers, before Rangers were drawn immediately after the Irn-Bru First Division side and paired with Motherwell.
With Ally McCoist's team now in the Third Division, the cup competitions are the only chance of an Old Firm derby taking place this term.
Ledley said: "I think most of the fans wanted to see that.
"As players, we will take anyone. It was close but not close enough.
"If we win, maybe we will see them in the next round or the next cup.
"It's a fantastic draw for us and we are just delighted to be at home.
"We haven't been at home for a while in the cups so we are happy with the draw.
"It's not going to be an easy game so we will just go out there and play our football and hopefully get the result.
"We played a couple of teams away from home last year and it was difficult for us so we are happy we got that home draw and we hope it's an advantage for us."
The Wales international admits Celtic will be determined to make amends for last season when they lost out to Kilmarnock in the final.
He said: "We were devastated that we didn't win it last year and we've got another opportunity now this year to win it.
"Hopefully we can achieve that but it's going to be a difficult game.
"Raith Rovers are going to be up for it and will make it difficult for us. It gives them an opportunity to play in front of a good crowd, in a good stadium and on a good pitch.
"It will be a hard game so hopefully we can have all our players fit for it and put a strong team out. We will have to be ready straight from the off."
Meanwhile, new goalkeeper Lubos Kamenar is keen to make an impact at Celtic after claiming his switch to Parkhead has already captured the imagination of his home nation.
The Slovakia international sealed a season-long loan from Nantes just before the transfer deadline on Friday and follows fellow countrymen Stan Varga and Lubo Moravcik in pulling on the hoops.
He told the club's website: "All of the people in Slovakia are proud of Moravcik and Varga and now I am following in their footsteps.
"There is huge interest back home in my country about the transfer because it's Celtic."
Kamenar will provide competition for Fraser Forster and Lukasz Zaluska for the number one jersey.
He added: "I know Fraser Forster who is a very good goalkeeper and he played last season, and I remember Lukasz Zaluska from Dundee United.
"I think they are both very good goalkeepers.
"For me, it's important that I work with good players and good goalkeepers and a good coach as that will improve me as a player.
"Celtic is a very good club and it's very important for me to improve in my career as well."
Kamenar was at Artmedia Bratislava when they faced Celtic in a Champions League qualifier in season 2005-06.
He said: "I remember that game was a full house.
"Celtic played very well and we lost here 4-0 but we had won in Slovakia 5-0 and we managed to go through to the next round.
"I have played at Inter Milan, Juventus and Galatasaray, but I think Celtic have the best fans I have ever seen in Europe.
"Every player would want to play for Celtic or play in a game involving Celtic because of them."
Source: team talk
Source: team talk