Fresh from holding Paris Saint-Germain in the league at the weekend,
Claudio Ranieri's side are not yet out of the Ligue 1 title race after coming from behind to draw 1-1 with PSG on Sunday, a result which left them five points off top spot.
And they are arguably the favourites to lift the Cup for the first time since 1991 following PSG's surprise exit to Montpellier in the last round.
The principality club, who are unbeaten in 2014, will travel along the Mediterranean coast to face Nice at the Allianz Riviera stadium, where they won 3-0 on league duty in December.
However, Ranieri will rotate his squad, with Argentine international Sergio Romero again set for a run-out in goal at the expense of Danijel Subasic and numerous other alterations likely, including a possible first start for January signing Dimitar Berbatov.
"The French Cup is not our objective," admitted the Italian. "Our objective is to qualify for the Champions League. But I play to win so I want us to qualify.
"It will be very difficult in Nice. We must forget about our 3-0 win there in the league. If we think this game will be identical, then we have already lost."
Opponents Nice, who last won the French Cup in 1997, have already beaten two top-flight sides on their way to the last 16 in the shape of Nantes and Marseille, with the latter being defeated 5-4 in a remarkable tie at the Stade Velodrome.
Only seven Ligue 1 clubs have made it to this stage, potentially leaving the path open for the likes of 2011 winners Lille and 2012 winners Lyon.
OL, who are already through to the final of the League Cup, will entertain second-tier Lens on Thursday, while Lille, third in Ligue 1, are at home to another second-tier side in Caen.
Transformed since the return as coach of Rolland Courbis, Montpellier's 2-1 win at PSG last month is the standout result of their unbeaten 2014 so far.
They are in action on Tuesday away to Cannes, a club who were in the top flight less than two decades ago but are now in the fourth-tier amateur ranks.
Nevertheless, Cannes stunned Saint-Etienne in the last 64, beating Les Verts on penalties, so Montpellier will not take their opponents lightly.
On-loan AC Milan forward Mbaye Niang will be on the bench at kick-off, though, as a punishment after a brush with the law last week.
Niang will appear in court later this month after crashing his Ferrari in Montpellier last weekend, despite not having a valid driving licence.
Cannes are one of four clubs from out of the professional ranks still in the running, as Moulins and Sete meet each other while L'Ile-Rousse entertain top-flight Guingamp.
The tiny Corsican side, from the fifth division, caused a sensation in the last round when they eliminated the holders Bordeaux in a penalty shoot-out.
