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And Hargreaves believes that Unai Emery can bring the best out of Elliott in the next few seasons after his transfer to Villa Park, which is a loan initially with an obligation to buy.
"I think technically he’s fantastic," Hargreaves said.
"Centrally, he’s a fabulous player."
"[Last season's loanees] Marcus Rashford and Marco Asensio were brilliant for this Aston Villa team," the former England international added.
"I think technically he’s fantastic, he hasn’t had the opportunities at Liverpool obviously, because they had so many players
But I think centrally, he’s a fabulous player."
Elliott featured 149 times for Liverpool, mostly coming off the bench, and scored 15 goals in that time before joining Aston Villa for a fee of around $47 million (£35 million).
"When I joined Liverpool in 2019 it was a dream come true for me and my family," Elliott said in a statement when he left Liverpool in the summer.
"As a young child, I traveled the world supporting the team as a fan and words will never be able to explain the feeling I had when I pulled on that famous red shirt for the first time as a player.
"Over the course of the last six years I've experienced so much and grown from a young 16-year-old boy into a man during my time at the club.
"Growing up, I could never have imagined that I'd go on to play 150 games for my boyhood team, winning seven major trophies and culminating in being part of the squad to have won the Premier League last season with such a special group.
"Thank you to everybody at the club for welcoming me from the very first day I arrived, and for looking after me ever since."
Liverpool.com says: Elliott has a huge amount of talent but he needs to play every week in order to fulfill that
At Aston Villa, he should get the opportunity to do just that