Ronald Koeman's men overcame Cornella in the third round to set up a tie with Vallecano, who have already beaten Teruel, Haro Deportivo and Elche in this season's tournament.
Rayo Vallecano's promotion prospects are certainly looking good as the business end of the season approaches, although their six-game winning streak across all competitions was recently ended by fellow high-flyers Mallorca on Saturday.
Andoni Iraola's men are now eight points adrift of the automatic promotion places, but a spot in the playoffs is certainly on the cards for a Vallecano side who last plied their trade in the big time during the 2018-19 campaign.
As far as their Copa del Rey fortunes are concerned, this week's hosts scraped by against Tercera Division side Teruel in round one but have since eased past Haro Deportivo and La Liga relegation candidates Elche - with former Manchester United winger Bebe scoring the opener in that one.
The last time that Vallecano advanced past this stage of the competition was back in the 2001-02 season - where Real Madrid dumped them out in the quarter-finals - and Villarreal eased to a 2-0 win over the Segunda Division side in the round of 16 last year.
A struggling Elche side were also the most recent victims of Barcelona, who are slowly closing in on the two capital sides in the race for La Liga glory.
Koeman's side enjoyed their second 2-0 victory in a matter of days as Frenkie de Jong and Riqui Puig both struck against Elche, with that result seeing Barcelona remain in third in the standings - 10 points behind current leaders Atletico Madrid, who have a game in hand.
La Blaugrana will need nothing short of a miracle to dethrone Diego Simeone's men now, but they have undeniably improved in the past couple of months and now boast nine wins from their last 12 in all competitions - including six from their last seven.
However, Barcelona did not have it all their way against Cornella in last week's Copa del Rey encounter, as the third-tier side forced extra time against a much-changed Blaugrana outfit, but late goals from Ousmane Dembele and Martin Braithwaite eventually saw the Catalan giants advance to the fourth round.
Furthermore, Barcelona have never failed to advance past the round of 16 in the Copa del Rey since the 2009-10 campaign, and Gramenet were the last team from a lower division to knock Barca out back in 2004.
Barcelona have eased to victory in their past 13 meetings with Vallecano - scoring a whopping 56 goals in that run before the hosts were relegated from La Liga once again in 2019.
Rayo Vallecano Copa del Rey form: WWW
Rayo Vallecano form (all competitions): WWWWWL
Barcelona Copa del Rey form: W
Barcelona form (all competitions): WWWLWW
Vallecano lost central defender Emiliano Velazquez to injury against Mallorca - by which point they had already shipped three goals - and he will certainly miss out here.
Esteban Saveljich should therefore take his place in the backline for Iraola, who himself was sent off at the weekend for protesting.
Meanwhile, wantway Barcelona talisman Lionel Messi is back for this game after serving a two-game suspension for his red card against Athletic Bilbao, and it would not be a surprise to see him make an immediate return with Antoine Griezmann due a rest.
Sergino Dest shook off a minor injury to make the bench against Elche but has been ruled out of this one, while the 20-year-old's fellow right-back Sergi Roberto is not thought to be too far away from a return to action.
Rayo Vallecano possible starting lineup:
Dimitrievski; Advincula, Catena, Saveljich, F. Garcia; Suarez, Comesana; Palazon, Trejo, A. Garcia; Bebe
Barcelona possible starting lineup:
Neto; Mingueza, Lenglet, Araujo, Firpo; Busquets, Pjanic, Puig; Trincao, Braithwaite, Messi
We say: Rayo Vallecano 1-3 Barcelona
Barcelona can expect some joy against a leaky Vallecano backline which has been depleted by the loss of Velazquez, although the hosts have already dumped one top-flight side out of the tournament and cannot be taken lightly. Nevertheless, the imminent return of Messi is certainly a welcome boost for the Blaugrana, and they should book their spot in the quarter-finals with minimal difficulty this week.