Castille has been on trial with the club and scored for the reserves last week in their 2-2 draw with Newcastle. Idrizaj has signed from Austrian club Linzer ASK.
"I have always been a Liverpool fan and it is a dream come true to play for them.
"If you get a chance to go to Liverpool on trial then you have to take it. You cannot ingore a trial with the reigning Champions League winners. I would even have swam across the channel just to take part." said Idrizaj.
Both players will play for the reserves against West Brom at the Hawthorns tonight.