The 18-year-old joined City from Feyenoord in the summer of 2011 and Rovers manager Michael Appleton said that he feels "lucky" to have brought him in on loan.
"He's going to be a Premier League player for the next 15 or 20 years - I feel lucky that we've got him," Appleton told BBC Sport.
"I've certainly brought him here to play. What we've got at the moment is a back four who are playing very well at the minute, so they'll all be expecting to play every week.
"However if there's a situation where people get knocks or look as if they are lagging a bit and need a rest, then Karim can step into that mark."
Rekik has made three appearances in all competitions for City.