The 21-year-old requested a loan move to regain first-team football and his availability will be a big boost for Coventry as they aim to secure their Championship status.
The Sky Blues are just 2 points above the drop zone with 9 games remaining.
"Kasper has shown this season that he has all the attributes to be a top-class Premier League goalkeeper and I have no doubt he will be a very valuable addition to the squad," Coventry boss Chris Coleman told the club's official website.
"He has a great ability and strength, plus he has age on his side. The future is certainly bright for him."