Dutch defender Rekik, 17, joined City in the summer after coming through the youth system at Feyenoord and 20-year-old Italian forward Scapuzzi has made two appearances for City, as well as nine on loan for Oldham earlier this season.
Pompey boss Michael Appleton said: "Karim can play at left-back or as a left-sided centre-half. He’s comfortable on the ball and has the right temperament to be at a club like Manchester City.
"Luca is a good footballer who can play out wide or up front. He’s already got Football League experience at Oldham."