Jurgen Klopp has hailed Trent Alexander-Arnold's "relentless" attitude at Liverpool and challenged the club's fans to come up with a song for him.
The England right-back extended his stay at Anfield by signing a new five-year contract on Saturday , keeping him on Merseyside until 2024.
Alexander-Arnold has become a key member of Klopp's Premier League-leading side since debuting in October 2016 and will now hope to help deliver a first title to Liverpool in 29 years this season.
Klopp is disappointed that the 20-year-old does not yet have a terrace chant on the Kop, although he believes one particular line of the renowned "allez, allez, allez" song relates to the defender, from whom he expects further development.
"With Trent, the most exciting thing about him is that the questions you ask about him always have a very positive follow-on," Klopp told Liverpool's official website.
"[You ask:] 'Is he a fantastic player?' Yes! 'But can he get even better?' Absolutely - and he will!
"He is such an amazing person, but I think sometimes maybe a little under the radar for his quality and technical abilities. He is so respected and admired in our dressing room, you would not believe.
"I know coming from the city brings extra pressure and burden, but he embraces this and thrives off it. Liverpool supporters love him as 'one of their own', although I have noticed he doesn't have a song from the fans yet, so maybe that is something they can work on. Wow, does he deserve one.
"Trent is one of the most relentless professionals I have met when it comes to focusing on getting better each and every day. This is not to compare with any legend past or present, because he will make his own story.
"As a player for Liverpool, he is the embodiment of the sentiment 'we're never gonna stop'."
Alexander-Arnold is currently out injured, but Liverpool's title bid will continue against Crystal Palace on Saturday and, ahead of that match, Klopp suggested neutral fans - including Everton supporters - might be backing his side .
"In Manchester, there are probably not a lot of Liverpool supporters," he said.
"Unfortunately I don't know enough people in England and the people I do know - even if they are Evertonians and know me personally - they think: 'If not us, then you can win it'. It is still Liverpool [the city].
"But it is not a surprise that people in Manchester might not want us to win it."