Sport says the Saudi Pro League club want to sign the midfielder immediately this week.
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Prim is off contract in June, but Al-Qadisiyah want to take the 18 year-old now rather than secure him to a Bosman arrangement.
Prim has battled for regular minutes with Barca Atletic this season and in talks he has been assured by Al-Qadisiyah coach Michel of a regular game in the SPL.
Prim was added to Barca's Champions League squad at the start of the season.