Bradley starred in place of Alexander-Arnold after the Engand man injured his knee last month, bagging a clean sheet and providing an assist on his first Premier League start against Bournemouth.
"He’s done a credit to himself and all the hard work he has put in," Alexander-Arnold told the club website. "I think the way he stepped up and performed was incredible.
"We see it day in and day out in training, how good he is and how good the rest of the young lads are. It’s a very good time for the academy. It’s very good to see."
He also commented on his own experience of progressing from the academy: "I never really thought about it back then. Still now, you’re just focused on breaking into the team, performing and being a part of the first team. You’re so focused on that - you don’t have time to think about anything else.
"I’m sure that’s what the young lads are doing right now. They are just wanting to soak up as much information as possible, and be as good as they can, in and around the lads."
Alexander-Arnold will be available for this weekend's game against Burnley at Anfield.