The right-back has been out for almost a month due to a hamstring injury suffered in the Premier League win over Aston Villa and is racing back to fitness ahead of the midweek clash with Leicester.
Lijnders, filling in for manager Jurgen Klopp in the pre-game Carabao Cup media duties, explained that no decision has been made on whether Alexander-Arnold will feature in the third-round clash at Anfield.
“Trent trained yesterday with us,” he told the club website.
“But it was just in the rondo and the ball possession with the counter-pressing, but he was outstanding. You see him instantly, of course.
“He is with the team training, I am not sure if he will be ready, we will see today.
“But then if we speak about Trent we have to make a compliment to Joe Gomez because the way he played the role, played the role in his way but still being able to come inside as well, was just incredible.
“His level and attitude, just a big compliment to him because you are replacing one of the best full-backs in the world. He did really, really well. That’s good and shows a lot about our squad as well, that we can have that.”