Meanwhile, their recently-promoted opponents head into the encounter with the champions having prevailed in two of their last three matches.
With the dust having settled after Bolingoli's high-profile misdemeanor, Celtic boss Neil Lennon is now tasked with trying to get his squad back up to speed in the top flight.
A nine-day gap after the draw at Kilmarnock was not ideal for the defending champions, but they would have taken heart from Rangers slipping up at Livingston last weekend.
Having breezed through their Champions League qualifier in midweek, Lennon will be much more optimistic about the task in hand as they bid to close the gap on their fierce rivals and Hibernian.
Although speculation will persist regarding the future of Odsonne Edouard, the in-demand Frenchman now has four goals from his opening three appearances this season.
However, aware that the squad requires adequate backup for their star man, Lennon will want to see Albian Ajeti hit the ground running after a frustrating year at West Ham United.
Like what Celtic are having to deal with concerning Edouard, Dundee United face the same issues with regards to the long-term future of Lawrence Shankland.
Amid speculation of a transfer to French side Guingamp, Micky Mellon has to focus on keeping the team's form heading in an upward trajectory at the same time as assessing his short-term options in attack.
On the plus side, the Terrors have defeated Motherwell and Ross County without the help of their most prized asset, who has been nursing an injury since the beginning of the campaign.
Given the money which has been mentioned, Shankland is unlikely to return to the fold at this stage, but that may not matter to his Dundee United outfit, who have been brilliant in their first season back in the top flight.
Dundee United Scottish Premiership form: DWLW
Celtic Scottish Premiership form: WD
Celtic form (all competitions): WDW
Despite remaining as an unused substitute in midweek, Kristoffer Ajer is expected to be recalled to the starting lineup.
After his goal as a substitute last weekend, Nicky Clark will almost certainly be restored to the Dundee United XI.
Dundee United possible starting lineup:
Siegrist; Freeman, Connolly, Reynolds, Sporle; Bolton, Harkes, Butcher, Pawlett, Chalmers; Clark
Celtic possible starting lineup:
Barkas; Frimpong, Juillen, Ajer, Taylor; Brown, McGregor; Forrest, Christie, Elyounoussi; Edouard
We say: Dundee United 0-2 Celtic
The European fixture in midweek proved to be the perfect exercise for Celtic to regain some match sharpness ahead of what has the potential to be a testing encounter. Despite Dundee United seemingly being on the right track, however, it would come as a surprise if the visitors do not prevail in comfortable fashion.