The La Liga outfit overcame Valencia in the round of 16 to advance to this stage, while Almeria beat Osasuna on penalties to ensure that they would be present in the final eight of the competition.
Almeria have reached the quarter-finals of the Copa del Rey for the first time since the 2010-11 campaign, when they made it to the semi-finals before suffering a heavy defeat to Barcelona.
La Union were regulars in La Liga between 2007 and 2015 but are in their sixth straight season in the Segunda Division, finishing fourth in the second tier last term after initially struggling to make their mark.
Almeria are third in this season's Segunda Division, meanwhile, just three points behind leaders Mallorca, and there is no question that they will be eyeing a return to the top tier.
Jose Gomes's side have beaten L'Hospitalet, Numancia, Alaves and Osasuna to advance to the quarter-finals and will now be looking to claim another top-flight scalp to reach the final four.
The hosts will enter Tuesday's contest in strong form, having won five of their last six matches in all competitions, including a 3-1 success at home to Castellon in the league on Saturday.
Lopetegui's side are also in excellent form, winning each of their last five matches in all competitions, while three straight league victories has allowed them to move into third position in La Liga.
Sevilla have also been impressive in this season's Copa del Rey, beating Ciudad de Lucena, Linares Deportivo and Leganes in the early rounds of the competition before putting three unanswered goals past Valencia on January 27 to breeze through to the quarter-finals.
Los Nervionenses have won the Copa del Rey on five occasions, last lifting the trophy in 2010, while they reached the final of the 2017-18 competition before losing to Barca.
Lopetegui will not view this tournament as a priority as the team go in search of La Liga and Champions League glory, but they are arguably the second favourites to lift the trophy behind Barca.
Almeria Copa del Rey form: LLWWWW
Almeria form (all competitions): WWWDWW
Sevilla Copa del Rey form: WLWWWW
Sevilla form (all competitions): LWWWWW
Almeria's team is expected to have a similar look to the one that started the last-16 clash with Osasuna last week, with Juan Villar likely to be given the nod through the middle.
Almeria possible starting lineup:
Martinez; Bunuel, De La Hoz, Chumi, Akieme; Robertone, Petrovic; Appiah, Villalba, Lazo; Villar
Sevilla possible starting lineup:
Bounou; Vidal, Kounde, Gomez, Rekik; Rakitic, Gudelj, Jordan; Suso, De Jong, Munir
We say: Almeria 0-2 Sevilla
Almeria have done brilliantly to reach this stage of the competition, but it is difficult to back the second-tier side against a Sevilla outfit that are expected to have a number of first-team players on the field; we fancy the Europa League holders to book their spot in the semi-finals courtesy of a 2-0 win.