Adrian was a free agent after leaving West Ham United at the end of last season and was unattached until Liverpool came calling for him to serve as back up to Alisson Becker following Simon Mignolet’s move to Club Brugge.
Adrian spent six years at the Hammers, making 150 appearances in all competitions, until the arrival of Lucasz Fabianski in 2018 relegated him to the substitutes’ bench.
The 32-year-old made a quicker-than-expected debut for Liverpool last week in their opening Premier League game of the season against Norwich City after Alisson suffered a calf injury, and he continued to deputise for the Brazilian in Wednesday’s UEFA Super Cup against Chelsea.
Adrian proved to be the hero for Liverpool, saving Tammy Abraham’s spot kick to hand Liverpool the trophy following a 2-2 draw after extra-time.
Speaking ahead of West Ham’s Premier League game against Brighton and Hove Albion on Saturday, Pellegrini expressed delight at Adrian’s impact at Liverpool so far but admitted he would have liked to keep him at the club.
"I'm happy for him because he played a lot of years here at West Ham," Pellegrini told a news conference, reflecting on Adrian's display against Chelsea. "He's a very good goalkeeper.
"For different reasons, he couldn't find an arrangement to continue here. We wanted him here because not only is he a good goalkeeper, he's a good player for the squad also.
"He had some problems at the start of the season, so signing for Liverpool and having this performance, I'm very happy for him."
Adrian will continue in goal for Liverpool as they take on Southampton at the Saint Mary’s stadium on Saturday.