With Rangers now unassailable at the top of the table, Celtic will want to win as they look for a strong finish to a disappointing campaign.
Dundee United are now four points behind sixth-placed St Mirren in the league table, and the Arabs' chances of making it into the top half of the table for the split look faint.
Winless in two games, Micky Mellon's men head into this clash with the Celts on the back of a 1-1 draw at Kilmarnock last weekend.
That result followed on from a 4-1 defeat at Ibrox to Rangers, but prior to that Mellon's Terrors had managed to win 3-0 at home to Livingston, so consistency is clearly an issue.
Recent history is not on their side when it comes to facing Celtic, with United having lost their last nine matches against the Bhoys in all competitions.
They also have a problem scoring goals against the green half of the Old Firm, failing to score in seven of their last nine games against the Hoops in all competitions.
Skipper Mark Reynolds acknowledged this week that the players are missing having the fans in the ground for big games like this weekend's clash with Celtic.
The absence of crowd support might just drain a crucial edge from United's push for the top six, with just two games remaining before the split.
Reynolds still feels a top-six finish is possible, but United will need three points this weekend to have any real chance.
Celtic beat Aberdeen 1-0 at Parkhead last weekend, a result which was at least an improvement on their abject defeat at Ross County the week before.
The Celts should certainly take comfort from their recent history against United, as the Bhoys have scored at least three goals in seven of their last eight matches against the Terrors in all competitions.
Dundee United have scored in each of their last five games, though, so Kennedy's Bhoys will need to concentrate in defence if they are to avoid any unpleasant surprises at Tannadice.
The Hoops look very much like a team in transition at the moment, and a pretty dramatic rebuilding of the squad can be expected once this season is out of the way.
A win in Dundee would provide little to ease the pain of Rangers possibly clinching the title this weekend, but minds at Celtic must now be on the future.
Dundee United manager Mellon cannot call on Declan Glass, who is out for the rest of the season with an ACL injury.
Dillon Powers is expected to return from a head injury soon but did not feature against Kilmarnock last week.
Celtic striker Odsonne Edouard might well be somewhat distracted this weekend, given the continuing reports about his future away from Parkhead.
Reports have indicated that a £15m move to Leicester City looks to be the forward's likeliest option, though the 23-year-old has also been linked with Arsenal and Roma.
Defender Christopher Jullien, out with a knee injury since September, has posted some encouraging updates on social media about how well his recovery is progressing, but he is unlikely to feature again this season.
James Forrest is another long-term absentee, while Greg Taylor missed the win over Aberdeen after limping out of the defeat to Ross County with a muscle strain, and it remains to be seen whether he will be fit for the trip to Tannadice.
Dundee United possible starting lineup:
Siegrist; Smith, Edwards, Reynolds, Robson; Harkes, Fuchs, Butcher, Sporle; Shankland, McNulty
Celtic possible starting lineup:
Bain; Kenny, Welsh, Ajer, Laxalt; Brown; Turnbull, McGregor; Christie; Kilmala, Edouard
We say: Dundee United 1-2 Celtic
Dundee United look to be running out of momentum a little after a creditable first campaign back in the top flight.
While Celtic have had problems in recent times, they should still be too strong for the tiring Terrors.