Kyle Lafferty could return to the starting XI after overcoming a sickness bug and a problem with his back, according to Levein.
The Northern Ireland striker admitted a gambling addiction earlier this week, but Levein believes the former Rangers and Palermo hitman will be able to block out any taunts from fans - if there are any.
Levein added: “He has had plenty of stick in his career and it just washes over him. I think you might be surprised this time. I think many people might sympathise. It is not so much a club thing.”
Hearts will assess Lafferty before the match but his return to the starting XI would give the Jambos a much-needed boost.
Don Cowie will also undergo a late fitness test with the midfielder nursing a tight hamstring.
Levein’s opposite number Neil McCann is looking for his side’s second win of the season after picking up the three points at home to St Johnstone earlier this month.
Long-term absentee James McPake is still working his way back from a knee injury while Craig Wighton and Kostadin Gadzhalov are also likely to miss out.
Club captain Darren O’Dea returns from suspension, but fellow defenders Josh Meekings and Julen Etxabeguren are set to be given more time to build up fitness after long-term injuries and are unlikely to make the squad.
However, Marcus Haber could make an appearance after overcoming an ankle problem while Sofien Moussa should return to the matchday squad as well.
Paul McGowan, who missed Dundee’s last game with Kilmarnock with a groin injury, could also feature.
Last five meetings: Hearts 1-0 Dundee; Dundee 3-2 Hearts; Hearts 2-0 Dundee; Dundee 0-1 Hearts; Hearts 1-1 Dundee; Dundee 1-2 Hearts.
Likely Dundee team (4-4-2): Bain; Kerr, Hendry, O’Dea, Holt; Deacon, Kamara, McGowan, Allan; Leitch-Smith, El Bakhtaoui. Subs from: Parish, Aurtenetxe, Waddell, Vincent, Spence, O’Hara, Williams, Wolters, Henvey, Moussa, Haber.
Likely Hearts team: (3-4-1-2): McLaughlin; Souttar, Hughes, Berra; M Smith, Randall, Callachan, Smith-Brown; Walker; Goncalves, Lafferty. Subs from: Hamilton, Nowak, Grzelak, Buaben, Martin, Milinkovic, Stockton, Currie, Henderson, Cowie.
Referee: Steven McLean
Odds: Dundee 5/2 Draw 5/2 Hearts 21/20 (Odds from SkyBet, correct at the time of writing)