The hosts are currently sitting in seventh place in the standings, while the Saints are three points further back in 10th position.
Match preview
Dundee have found victories hard to come by in recent times, having won just one of their last six matches in the top flight (D2, L3).
While a lack of wins may frustrate Tony Docherty, the Dundee manager would have been relieved to see his team rescue a point from Saturday's clash with Kilmarnock.
The Dee looked to be heading towards defeat when Kilmarnock scored two late goals to turn the game in their favour, before Joe Shaughnessy hit back in the 95th minute to ensure his side left Rugby Park with something to show for their efforts.
Despite salvaging a 2-2 draw from the weekend's away trip, Dundee have now conceded at least two goals in five of their last six games, highlighting a key area for improvement in the new year.
Although they are unbeaten in four matches against St Johnstone, their hopes of claiming a victory may be tempered by the fact the last three head-to-head meetings have finished all square.
St Johnstone, meanwhile, will also be desperate to clinch all three points after enduring a three-game winless run since edging out Hibernian on December 16.
After squeezing past Hibs, the Saints went on to lose back-to-back matches against Rangers and Kilmarnock, before they played out a goalless draw in last Wednesday's meeting with Livington.
Those three results ultimately prolonged their struggles on the road, having failed to win any of their 10 away league games this season (D4, L6), leaving them with the worst away record in the division.
After scoring just two goals in their 10 league road trips, St Johnstone know they need to discover a cutting edge in the final third if they are to win a Scottish Premiership away game for the first time since May.
Craig Levein's side will head back on their travels for their first match of the new year, and they will be keen to extend the small one-point gap keeping them above 11th-placed Ross County.
Dundee Scottish Premiership form:
L
D
L
W
L
D
St Johnstone Scottish Premiership form:
W
D
W
L
L
D
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Team News
Dundee forward Diego Pineda is set to miss a second straight game due to a knock, while fellow Mexican Antonio Portales remains sidelined with a hamstring injury.
The hosts also have doubts over the availability of defender Ricki Lamie and striker Zach Robinson, who will both have to be assessed ahead of Tuesday's fixture.
Malachi Boateng and Zak Rudden could be recalled to the starting lineup after the pair dropped down to the bench for Saturday's draw with Kilmarnock.
As for the visitors, they could be without the services of Ross Sinclair, Sam McClelland, Ali Crawford, Cammy MacPherson and Drey Wright.
Maksym Kucheriavyi is also a fitness doubt after he was forced off in the first half of last Wednesday's goalless draw against Livingston.
Levein will be hoping to have Ryan McGowan and Fran Franczak available after the pair missed out against Livingston through illness.
Dundee possible starting lineup:
Carson; Donnelly, Shaughnessy, McGhee; Mulligan, Boateng, Sylla, McCowan, Beck; Bakayoko, Rudden
St Johnstone possible starting lineup:
Mitov; McGowan, Gordon, Robinson; Franczak, Phillips, Smith, Gallacher; Carey, Clark; May