Manager Dave Jones was facing a goalkeeping crisis with number one David Marshall away on international duty with Scotland but Enckelman, himself called up by Finland, has pleaded with his national side to be made available for the Bluebirds.
However, City remain without a host of star names due to the international schedule including Joe Ledley, Ross McCormack and Gabor Gyepes, while several younger players are also away on Under-21 duty.
Elsewhere, as many as eight Bluebirds players went down with a bug last week, forcing Chris Burke to drop from the starting XI to the bench for Saturday's 4-0 triumph over Scunthorpe and Ledley to come off at half-time.
It remains to be seen whether Burke will feature from the off this time around although Jones is determined to put out his best possible XI.
He told the club's official website: "We've been hit by international calls but we'll put out our strongest team because we take this competition seriously. There could be opportunities here for Academy lads. In situations like these, one person's loss is another person's gain."