Downing played with the 18-year-old for a season at Blackburn Rovers, where the young attacker blossomed into a senior footballer.
Elliott is now back at Anfield and Downing believes he has a bright future ahead of him.
"He found himself playing in the middle, he didn't do that a lot for us at Blackburn, maybe once or twice. But he took the position at the start of the season, playing ahead of some big players," said Downing to the club's website.
"You can see his ability for a young player, he's quite mature for his age; the way he plays and his positioning, he's not a young player who runs everywhere and is undisciplined, he's quite mature for his years.
"Going to Liverpool and being coached by Klopp before he went on loan is massive for him because he's playing with world-class players every day, the standard will be unbelievable really.
"Barring injury at the start, he would have had a massive run in the team and you've got to give him credit for that. He's definitely got the ability."
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