The France international's season appears to be over after he suffered a knee injury in Saturday night's 1-1 draw with Espanyol at Cornella
Varane has established himself at the heart of the Blancos defence this season but is now expected to miss Friday's clash with city rivals Atletico after being forced off with a knee injury just 19 minutes into Saturday's Liga clash with Espanyol.
With Pepe seemingly having been ostracised for publicly criticising Jose Mourinho over his treatment of benched captain Iker Casillas, Albiol is now in line to replace Varane in the starting line-up for the Copa final.
"It is unfortunate for that to have happened to a team-mate, whether it was Raphael or anyone else," the Spain international is quoted as saying by his club's official website.
"It could be me or one of my team-mates who replaces him, so we must all train well and be ready for if the coach decides that we are playing."
Saturday's 1-1 draw with Espanyol signalled the end of Madrid's reign as champions, as it left Jose Mourinho's men seven points behind Barcelona with just two games left to play.
Given los Blancos also saw their Champions League hopes ended by Borussia Dortmund last month, Albiol is now desperately hoping that they can finish a disappointing campaign on a high with a Copa success.
"We have to think about Atletico and now we have to prepare ourselves because on Friday we can win a major title for the fans and the team," the centre-half explained.
"The coach, like us, wants to win that title. It was a disappointment not to be playing in the Champions League final, but what we have to do now is win on Friday."
Madrid's meeting with Atletico at the Santiago Bernabeu kicks off on Friday at 21:30CET.