The Hoops have won their past 14 matches as they moved top of the Scottish Premier League and progressed to the final of the League Cup after dispatching Falkirk in the semi-final.
Now Neil Lennon's side have Inverness in their sights as they aim to make the quarter-finals of the Scottish Cup.
However, Inverness have form against Celtic in the Scottish Cup having famously knocked the Hoops out of the competition in 2000 when they were a First Division side, a feat they repeated in 2003.
And Welsh international Ledley knows they face a difficult task against Terry Butcher's side, who also ended their title hopes last season with a 3-2 win at the Caledonian Stadium.
"We're on a good run at the moment and we always say it, but we have to take each game as it comes," Ledley said.
"It's good knowing we have a final coming up but we're forgetting about that for the moment.
"We're away to Caley Thistle at the weekend in another cup tournament, and we want to win that one too.
"It's going to be difficult, it always is up there, and Caley will be desperate to progress in the Cup themselves. But we're looking strong just now and we have a lot of players back from injury."
Inverness are also undefeated in seven matches and manager Terry Butcher is confident of causing an upset.
"The boys know the importance of the game, they know the opposition and how well Celtic are playing at the moment because they are on an excellent run themselves too," Butcher said.
"But runs have to come to an end and we want to end Celtic's run and make progress in this competition.
"To do that we've got to be at our best and we have got to give it everything. We will certainly have a go."
Rivals Rangers also have a difficult task to progress to the quarter-finals as they host fellow SPL side Dundee United at Ibrox on Sunday.
And after being knocked out of the League Cup earlier in the season full-back Sasa Papac, who is set to quit Ibrox at the end of his contract this summer, is determined to finish his career on a high with an appearance in May's Scottish Cup final.
"The Dundee United game is a very important one for us because we can only win two trophies now this season," the Bosnian international said.
"We have to be focused and keep our concentration because we all want to get through to the next round.
"You train all of your life to win titles and cups and if, at the end of your career, you have medals that is great.
"That is why we must give everything against Dundee United and I hope we can get to another final."
The Gers will have to learn to live without top scorer Nikica Jelavic, who sealed a move to Everton in midweek, while fellow strikers Kyle Lafferty and Steven Naismith remained sidelined through injury.
Elsewhere on Saturday, Aberdeen host First Division Queen of the South, there is an all SPL tie between Hibernian and Kilmarnock at Easter Road and St Mirren take on First Division league leaders Ross County.
Hearts host St Johnstone at Tynecastle on Sunday in an all SPL clash.
Fixtures (1500 unless otherwise stated)
Saturday
Inverness CT v Celtic (1245), Aberdeen v Queen of the South, Ayr v Falkirk, Hibernian v Kilmarnock, Motherwell v Morton, St Mirren v Ross County
Sunday
Rangers v Dundee United (1215), Hearts v St Johnstone
Source: AFP
Source: AFP