Alcorcon, whose stadium to the south of the capital will have its capacity expanded to around 4,000 for the first leg, play in the same league as Real Madrid's youth team Castilla.
"It's inevitable that you get carried away," Alcorcon coach Juan Antonio Anquela told sports daily Marca on Monday.
"We are aware that it is like the story of Cinderella, where at midnight we will return to crude reality, but no one is going to stop us from having our dance with the prince. We have won this right on our own merits."
Alcorcon can take heart from last season's competition when a side from the same division, Real Union, managed a shock result over two legs to knock out Bernd Schuster's Real at the same stage, on the away goals rule.
Anything less than a comfortable win would increase the pressure on Real coach Manuel Pellegrini, whose side have failed to impress recently.
"We have been made to look foolish in this competition before so we will be approaching it with the same mentality as if it were the Champions League," Real goalkeeper Iker Casillas told a news conference.
Another Segunda B side, Marbella, will be looking to spoil Quique Sanchez Flores's debut as Atletico Madrid coach when they travel to the south coast on Tuesday.
Atletico, who sacked Abel Resino on Friday, are 17th in La Liga with one win from their last 11 matches in all competitions.
"The (immediate) objective is to lift the morale of the players," Sanchez Flores said at his presentation on Monday.
Segunda B's Cultural Leonesa host holders and la Liga leaders Barcelona on Wednesday, and last year's finalists Athletic Bilbao visit second division Rayo Vallecano on Wednesday.
The second legs are scheduled for the week beginning November 9.
