Celtic come into this game on the back of a 3-0 win over Hamilton Academical on Saturday at the New Douglas Park.
Goals from French striker Odsonne Edouard, Scotland international Leigh Griffiths and midfielder David Turnbull secured the win for Neil Lennon's Celtic.
Dundee United, on the other hand, drew 1-1 against Motherwell on Saturday at the Tannadice Park.
Former Celtic attacker Tony Watt put Motherwell ahead early in the first half, only for striker Nicky Clark to score the equalizer for Dundee United in the dying embers of the second half.
Celtic vs Dundee United Head-to-Head
In 46 previous encounters between the two sides, Celtic hold the clear advantage. They have won 31 games, lost three and drawn 12.
The two clubs last faced each other earlier this year in the Scottish Premiership, with Celtic beating Dundee United 1-0.
A second-half goal from former West Ham United striker and Switzerland international Albian Ajeti ensured victory for Celtic.
Celtic form guide in the Scottish Premiership: D-D-W-W-W
Dundee United form guide in the Scottish Premiership: L-L-D-W-D
Celtic vs Dundee United Team News
Celtic manager Neil Lennon will be unable to call upon the services of Scotland international James Forrest, who is out with an injury. There are doubts over the availability of Israeli defender Hatem Abd Elhamed.
Injured: James Forrest
Doubtful: Hatem Abd Elhamed
Meanwhile, Dundee United will be without young midfielder Declan Glass and attacker Logan Chalmers, who are both nursing injuries.
Injured: Declan Glass, Logan Chalmers
Celtic vs Dundee United Predicted XI
Celtic Predicted XI (4-3-3): Conor Hazard, Jeremie Frimpong, Nir Bitton, Kristoffer Ajer, Greg Taylor, Ismaila Soro, Callum McGregor, David Turnbull, Ryan Christie, Leigh Griffiths, Odsonne Edouard
Dundee United Predicted XI (4-4-2): Benjamin Siegrist, Liam Smith, Mark Connolly, Mark Reynolds, Adrian Sporle, Paul McMullan, Calum Butcher, Jeando Fuchs, Luke Bolton, Marc McNulty, Lawrence Shankland
Celtic vs Dundee United Prediction
Celtic have struggled to match their lofty standards this season, and sit second in the league table, 16 points behind arch-rivals Rangers.
Neil Lennon's side do have three games in hand, but it will be difficult to catch Steven Gerrard's dominant Rangers. The Bhoys could also lose star attacker Odsonne Edouard soon, with Juventus and Arsenal linked.
Dundee United, on the other hand, sit fifth in the league table. Their innovative scouting methods have been appreciated, and Micky Mellon's side could prove to be a problem for Celtic.
Celtic have the players to secure a win in this fixture, but Dundee United will not make it easy for the champions.
Prediction: Celtic 2-1 Dundee United