The visiting Nerazzurri, meanwhile, have not lifted the trophy for a decade and now aim to take another step towards a first domestic double since the Jose Mourinho era.
Inter travel to Florence having been denied all three points late on in an absorbing clash with Serie A rivals Roma. The two Scudetto contenders shared four goals at the Olimpico on Sunday, as Antonio Conte's side managed to maintain second place in the table ahead of the Giallorossi.
Once again, former Real Madrid wing-back Achraf Hakimi starred in the capital, providing a constant threat on the right flank and popping up with another fine goal - using his weaker left foot to place an unstoppable shot past Pau Lopez and give Inter the lead.
Failing to hang on to that advantage now means that the Nerazzurri have picked up only a point from their past two league games, following a run of eight straight wins.
Fatigue accumulated because of their extended summer schedule has been posited by Conte as the reason for such a downturn, with important players such as Romelu Lukaku and Nicolo Barella rarely rested, while veterans Arturo Vidal and Samir Handanovic have started to show their age.
They now enter the Coppa at the fifth round stage due to their previous European commitments, which were brought to an end by Champions League failure before Christmas - perhaps allowing a greater focus on claiming the cup in spring.
Despite the continuing fixture congestion which has seen most Italian sides playing three times a week either side of a brief winter break, Conte is likely to name a relatively strong XI at Stadio Artemio Franchi, as he comes head-to-head with fellow former Azzurri boss Cesare Prandelli.
Since the decisive goal of Portuguese forward Nuno Gomes last enabled Fiorentina to lift the Coppa Italia after a two-legged victory over Parma in 2001, the grand old Tuscan club have enjoyed and endured many highs and lows.
Cup success has eluded them in the intervening decades however, so on Tuesday the Viola will be aiming to continue a run which has so far seen them knock out Padova and Udinese in the third and fourth rounds respectively.
They prepared for an intimidating fifth round test against Inter by sealing a valuable league win at the weekend - turning over Cagliari at home, thanks to the heroics of two of their best performers of a trying season so far.
Serb striker Dusan Vlahovic's strike helped coach Prandelli - who has overseen an uplift in Fiorentina form since his return to the dugout in December - seal victory, following indomitable goalkeeper Bartlomiej Dragowski's earlier penalty save.
Now into the top half of the Serie A table after a run of seven points from four games, the Viola can concentrate on a challenging cup clash with many pundits' title favourites.
Always pragmatic, Prandelli has already lost fringe players Patrick Cutrone - who has returned to parent club Wolverhampton Wanderers - and Pol Lirola (heading to Marseille) during the transfer window and claims that thinning his squad can be taken as a positive.
Highlighting that it can often be counterproductive to have too many players waiting in the wings - certainly a problem in Fiorentina's unwieldy and ill-balanced squad - the experienced tactician wants to focus on quality rather than quantity when it comes to recruitment in the coming weeks.
With Vlahovic and even the so-far underwhelming Jose Callejon now starting to fire, perhaps the solutions to their previous problems do exist within. Certainly, the forward pair will be crucial in the attempt to pull off a cup shock this week.
Fiorentina Coppa Italia form: WW
Fiorentina form (all competitions): DDWDLW
Inter Milan form (all competitions): WWWWLD
The former Juventus manager could enact a significant turnover in his XI ahead of the crucial Derby D'Italia against his former club next Sunday.
His 3-5-2 could therefore feature Andrei Radu in goal, with Andrea Ranocchia and Aleksandr Kolarov coming into the back three. In midfield, Roberto Gagliardini could replace Barella and Christian Eriksen may even make a possible farewell appearance for the Nerazzurri.
Most likely matching up against Inter in a 3-5-2, 'cup keeper' Pietro Terracciano would come in should Dragowski be rested, with Borja Valero and Erick Pulgar competing for one spot in the midfield three alongside improving Sofyan Amrabat and early-season star Gaetano Castrovilli.
Christian Kouame is expected to support in-form Dusan Vlahovic in attack, with Patrick Cutrone having returned to Wolves.
Fiorentina possible starting lineup:
Terracciano, Milenkovic, Quarta, Caceres; Igor, Amrabat, Pulgar, Castrovilli, Biraghi; Kouame, Vlahovic
Inter Milan possible starting lineup:
Radu; Skriniar, Ranocchia, Kolarov; Young, Gagliardini, Sensi, Eriksen, Perisic; Martinez, Sanchez
We say: Fiorentina 1-3 Inter Milan
The impressive squad depth available to Inter means that even if Antonio Conte operates a rare rotation on Tuesday, the XI to face Fiorentina will be more than capable of sealing progress to the quarter-finals.
The improving Viola should put up a fight, but their expensively-assembled visitors do not have the 'distraction' of continental football in the coming weeks and can instead focus their energies on claiming the Coppa as part of a potential domestic double.