Manuel Pellegrini is happy to see Adrian making an immediate impact at Liverpool but would have liked to have kept the goalkeeper at West Ham.
Adrian left London Stadium as a free agent at the end of last season and spent the summer out of work, at one point, training with a semi-professional club in his homeland of Spain.
However, near the end of the window, Adrian signed for European champions Liverpool, replacing Simon Mignolet as Alisson's back-up.
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But an injury to Alisson in the Premier League opener against Norwich City saw Adrian quickly thrust into the action at Anfield.