The reigning Spanish champions have refused to comment on whether or not they are interested in signing the Wales winger.
The Wales international has been in sublime form in the past few months, and is continually being linked with a transfer away from his current club.
Nevertheless, Karanka has refused to comment on whether Madrid could make a move for the winger at the end of the season.
"Bale is another team's player and I cannot say anything about him. He is a classy player, though," Karanka said at a press conference.
Jose Mourinho's assistant then went on to discuss the situation of Pepe, who has seemingly lost his starting berth to Raphael Varane, and insisted that the Portugal international is still an important player for Madrid.
"Pepe is very important for us and will continue to be important. He is still coming back from an injury. If someone's happy for Varane, it's Pepe," Karanka explained.
Karanka also had his say on los Blancos' title chances, and admitted that the club might have to settle for second place.
"Winning the Liga is nearly impossible. We have to focus on finishing second in the table," he stated.
Madrid currently sits third in La Liga, trailing second-placed Atletico Madrid by two points.