The 32-year-old has been first choice in Klopp’s midfield this season, limiting the game time of expensive summer signings Fabinho and Naby Keita.
And Milner was at his influential best in the middle of the park in the English capital at the weekend as Liverpool FC left with a vital point.
The former Leeds United talent appeared to have scored a 61st-minute winner when he seized upon a loose ball in the Arsenal penalty area and steered a finish past Bernd Leno.
However, Milner was denied the status of match winner when Alexandre Lacazette scored an equaliser from an acute angle with eight minutes to play in north London.
The retired England international contributed more than just his goal with a talismanic performance in the middle of the park for Liverpool FC.
The two-time Premier League winner won four aerial challenges, made three successful tackles and completed 39 of his attempted 46 passes.
Klopp, whose side dropped from second to third after the stalemate, was thrilled with his vice captain’s performance in Liverpool FC’s 1-1 draw with Arsenal.
“Milly is like wine – a very good red one. I’m not sure if Leeds is famous for wine? He’s getting better,” Klopp is quoted as saying by Sky Sports.
Klopp added: “I think Millie should buy all of the newspapers and read this.
“I would like it if you write a story about James Milner, I will like it. Obviously someone might write that he will have to play for England again. That’s a really nice idea.”
Milner could be rested for Liverpool FC’s trip to Serbia in the Champions League on Tuesday night as the Reds look to secure their third win of the Champions League campaign against Red Star Belgrade.
Speaking to the media after the 1-1 stalemate, Klopp revealed Milner gave his team-mates a stern telling off for their first-half performance at Arsenal.
“You have a compact formation, you force [Arsenal] to pass the ball somewhere – that’s pressing, it’s not that complicated,” said Klopp.
“The best way is to do it right from the first moment and then you can build on that, but we didn’t do it right from the first moment.
“That means there’s a time that it’s not there and we all felt like, ‘What the heck is here?’
“Milly was the one who saw it first and was quite – how can we say, was not happy – was animated. That’s good. That’s how it is in a dressing room, there is a lot of men, a lot of testosterone.
“One is talking – that’s me – and sometimes before I start talking the boys have a few words and that’s all. Milly is a proper leader.”
The former Newcastle United star is still waiting to win his first trophy as a Liverpool FC player since his free transfer to Anfield from Manchester City under Brendan Rodgers in 2015.
Milner has scored 18 goals in 146 games over the past three and a half seasons at the Merseyside outfit.
Klopp has returned Milner to his favoured central midfield role after the ex-England star was used at left-back throughout the 2016-17 season.
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