Meanwhile, the home side welcome the defending champions to Rugby Park having suffered an opening-day setback at Hibernian.
Usually at this time of year, Celtic are distracted in trips across Europe as they bid to earn a place in the Champions League or Europa League.
However, with last season's competition still to reach a conclusion, it has left Neil Lennon to focus on life in Scotland, something which could prove to be the difference when it comes to trying to earn a 10th successive league title.
Five goals and 25 shots against Hamilton suggests that Celtic are already close to their best form, with potentially the toughest task coming behind the scenes as they bid to keep hold of Odsonne Edouard.
There is an inevitability about the Frenchman's eventual exit, but his treble last weekend may be enough to convince all the relevant parties that he should be kept in Glasgow for what could turn out to be an historic campaign.
From Kilmarnock's perspective, Alex Dyer has been left to assess the positive and negatives from succumbing to Hibernian at Easter Road.
Conceding a fifth-minute opener set the tone, and the slow start ultimately proved crucial as they lost out to opponents whom they will regard as rivals for a position in the top six.
With Celtic and Rangers to come in their next four fixtures, it was a defeat which Kilmarnock could ill-afford as they look to give themselves some kind of platform to work from heading into September.
However, Killie have emerged victorious in two of their last four home meetings with Celtic, while also only suffering 1-0 and 3-1 setbacks in the most recent corresponding games.
Although the lack of home fans will not help their cause, Dyer must hope that the recent head-to-head record provides his players with some belief ahead of what may feel like a daunting task.
Kilmarnock Scottish Premiership form: L
Celtic Scottish Premiership form: W
While Lennon could opt for the same starting lineup, the Northern Irishman has a number of selection dilemmas.
Olivier Ntcham is pushing for a start after only being used as a substitute last weekend, while new arrival Patryk Klimala will hope that his goal on his cameo outing will lead to a first start in Celtic colours.
Clevid Dikamona, who signed for Kilmarnock earlier this week, could be brought into the backline.
Kilmarnock possible starting lineup:
Rogers; Millen, Broadfoot, Findlay, Waters; Power, Tshibola; Burke, Kiltie, McKenzie; Kabamba
Celtic possible starting lineup:
Barkas; Frimpong, Jullien, Ajer, Taylor; Brown, McGregor; Forrest, Christie, Klimala; Edouard
We say: Kilmarnock 1-3 Celtic
Despite Kilmarnock potentially benefitting from getting 90 minutes in their legs, we can only see one winner here. Celtic are yet to begin their European schedule, and that will only play into their favour during the early weeks of the season.