The Hoops are on course to match the domestic double they claimed last season having won their past 14 domestic matches.
However, standing in Celtic's way for a place in the quarter-finals are an Aberdeen side that sits second in the Scottish Premiership and last weekend clinched a place in the League Cup final.
Aberdeen were also the last team to score against Celtic on domestic duty way back in November and the champions boss Neil Lennon is wary of the goal threat that Derek McInnes' side will pose on Saturday.
"They're very good on the counter-attack as they've got good pace in Jonny Hayes and Peter Pawlett, plus they have brought Adam Rooney in who knows how to play centre-forward and they have good experience in midfield so they are a confident team," Lennon said.
"We want to defend the cup
Aberdeen are obviously on a high from getting to the final of the League Cup but we are at home and we want to impose our authority on teams here.
"I think we've done that over the past four or five weeks so we'll be looking to go into this weekend with the same approach."
Celtic could be joined in the next round by bitter historical Glasgow rivals Rangers, who face fellow League One side Dunfermline in Friday's match at Ibrox.
The Scottish Cup represents Ally McCoist's side's last chance to shine on the biggest stage this season and striker Jon Daly insists the club are capable of going all the way.
The Irish forward, who helped dump Rangers out of the competition at the same stage last year when he was with Dundee United, hopes to fire Rangers a step closer to ending a three-year trophy drought in major knockout competitions.
"It's amazing that a year in football can change so much
This time last season I was getting ready to face Rangers in the fifth round, now I'm obviously playing for them," Daly, who won the cup with United in 2010, said.
"Every player wants to do well in this Cup because it's a fantastic competition to be involved in.
"To win it was fantastic and last year United were also unlucky at the semi-final stage not to go through.
"Winning the Cup meant a hell of a lot to me before - and we had a young squad then
Winning trophies is massive and you live in the here and now.
"What I have done in the past is in the past so I look forward to winning more medals
As long as we are in the Cup, we have a chance of winning it.
"It's all about how you perform on the day, so it's a massive game for us on Friday night and a great opportunity to get to a quarter-final."
Fixtures (1500 GMT unless otherwise stated)
Friday
Rangers v Dunfermline (1930)
Saturday
Celtic v Aberdeen (1245), Hibernian v Raith Rovers, Albion Rovers v Stenhousemuir, Alloa v Dumbarton, forfar v St Johnstone, Stranraer v Inverness CT
Sunday
Dundee United v St Mirren (1200)
Source : AFP
Source: AFP